Chabad Position #1 - The Rebbe was "chezkat Moshiach", (presumed Moshiach as per the Rambam’s Hilchos Melachim uMilchatonim). Since his passing from this world he remains a strong influence, perhaps (as taught in Tanya from the Zohar) even a greater influence than when he was with us physically. (The Tanya teaches that a tzadik's influence is greater after his physical departure as he's no longer bound by physical limitations.)
A corollary to this position says the Rebbe was Moshiach ben Yosef, whom the mystical sources teach starts the Redemption process but doesn't survive it and is followed later by Moshiach ben Dovid.
Chabad Position #2 - The Rebbe was "presumedt Moshiach" and remains so even after his physical departure (as taught in the Gemora Sanhedrin that candidates for Moshiach may come from those who are not among the living).
Everything the Rebbe said came true (public predictive statements), defining him as a true navi (biblical level prophet), therefore his statements on Moshiach and geulah must be treated as navua (biblical prophecy) - prophecies of a kosher prophet that have not yet been fulfilled.
Chabad Position #3 - The Rebbe was Moshiach tzidkaynu (our righteous redeemer) as confirmed by rulings of hundreds of rabbis and his demonstrations of navua (prophecy), as well as fulfilling most of Rambam's rulings on the actions Moshiach must fulfill (Mishneh Torah Hilchos Malachim uMilchatonim 11).
The Rebbe wrote as part of his navua (prophecies) that Moshiach would go through a time of pain and subsequently a time of being hidden. Therefore we must trust in Hashem and in the words of the Rebbe during this time of darkness and cannot define the Rebbe as having left this world.
Chabad Position #4 - The Rebbe is Moshiach tzidkaynu who is hidden from us at this time. He gave us the paths to follow and the final mitzvah campaign/focus to teach about Moshiach and the Geulah and focus upon them. Therefore we are obligated to continue in this area with maximum effort (and perhaps the only effort of mitzvah campaigns) to bring the Geulah to completion. Since Moshiach ben Dovid does not die, the Rebbe is not dead.
Position #5 - The Rebbe is Moshiach tzidkaynu who is hidden from us at this time. The Rebbe wrote in his prophecies that we have entered the time of the Geulah and "people must only see it and recognize it". Therefore, recognizing that this is the time of the Geulah we will begin to live according to the words of all of those who have written of how it will be during the Geulah, such as changing Rabbinic fast days to feast days. Geulah is here, open your eyes and see it and join us.
Position #6 - The Rebbe, Moshiach and Prophet, wrote about the levels of connection between the soul of Moshiach and Hashem, and how Moshiach's soul connects at higher levels than ever seen before in this world - bringing down a level of Hashem's light beyond what the world has experienced. Therefore, the Rebbe Moshiach, who is here although hidden at the moment, is not just the agent of Hashem in this world but the arm of Hashem in this world. And since Hashem is one, the arm of Hashem is...Hashem. Therefore the Rebbe, Moshiach and Prophet, is Hashem.
Now, most of Chabad holds position #1. It's a completely kosher position by everyone's understandings and evaluation. Further, the official Chabad organizations have been relatively forcefully purged of anyone not holding position #1 for the past 15 years (successfully). The stronger Moshiach positions are not tolerated by the official organs of Chabad Lubavitch (Merkos L’Inyanei Chinuch, Agudas Chasedi Chabad, The Shluchim’s Office, Kehot Publications, etc.)
Some in Chabad hold position #2, more so in Israel. This makes non-Chabad theological authorities a bit nervous and they'll challenge whether halacha holds at this time that Moshiach can come from among the non-living (it doesn’t). But they'll also grudgingly admit that holding this position is kosher (if not preferred).
Positions #3 and #4...are held by what are called Meshichists (Moshiach guys, often identified by wearing yellow Moshiach flag pins), more so by native Israeli Chabad than US or worldwide Chabad. In the US this is found almost solely in Crown Heights where it may be 25%, but that includes the Israreli Torah students studying there. The positions are problematic but not directly non-kosher according to major poskim and gedolim that have reviewed them. Meaning we wouldn't call the position mainstream Torah Judaism, but you can't define people who hold it as heretics. #3 people are handling out flyers that refer to the Rebbe Melech HaMoshiach, and #4's flyers talk only about geulah and may add Rebbe Melech HaMoshaich Chai Vekayam (lives forever).
People of position #4 make people of position #1 nervous, as Chabad as an organization is also concerned about people going off the deep end and about their image.
Position #5 is a real halachic problem. These people are stepping beyond contemporary orthodox Judaism (but they'll tell you the same could have been said about the Baal Shem Tov). We have no authority to make a halachic decision changing what should or should not be observed and await a true Sanhedrin (a great court of Torah sages), which may come about in our time or be created after the arrival of Moshiach. (It is not dependent on Moshiach and there have been several attempts in history to create a Sanhedrin, including a recent one.) People holding this position must be treated as non-observant Jews who have gone off the path. But they are problematic because they otherwise appear as Torah observant Jews.
Personally I would include them in my minyan like any other Jew who’s not properly observant and is involved in improper things. But I would not pray in their minyan and I certainly wouldn't talk to them about their position.
This is a small group of people and upon beginning such actions they are pushed away by the normative community (Chabad or otherwise). Small but they get attention due to the shock value. I’ve heard of a couple people like this in Crown Heights, and another small group (of 10 I think) in Australia.
Position #6 is absolutely treif and complete kefirah (being a heretic). These people are starting a new religion and may appear as religious Jews and practicing some Jewish rituals but they aren't praying to the same understanding of G-d as orthodox Judaism. A person who has personally stated that he holds such beliefs probably could not be included in a minyan.
NOW, Confused, where's all this leave you? Well, almost no shluchim / Chabad houses in the US hold anything other than position #1, and if they did they were pushed out. (There are a few exceptions.) In Israel the same is true but it's often position #2. No true major authorities have any serious problems with these positions (doesn't mean they like them, but that doesn't make them a halachic problem.)
Positions #3 and #4 are concentrated into Crown Heights and certain places in Israel (such as Tzfat) - which explains your encounter in Crown Heights. This is unfortunate and bad PR but the community as a whole doesn't really want to go shoving people completely out that may turn them out of Judaism.
Positions #5 and #6 have to be stayed away from. Fortunately they're few and their positions are clearly a problem and therefore easy to avoid. And yes they may also be living in a major Chabad community but are literally stayed away from.
As for web sites and not-major-authorities that want to rail against Chabad and look at a few nut jobs in the later positions as representing Chabad, they're also writing what they're writing sitting in Williamsburg or Bnei Brak in their ultra-kosher community with ultra-kosher services. The same type of people were known to write in the past that it's ASSUR (prohibited) to reach out to non-observant Jews because they might influence the kosher Jew in a negative way.