The Lubavitcher Rebbe never said he was Moshiach, or even that he was going to be Moshiach, but he said a lot of things that could easily be understood to imply that this would happen. Since during his life all his chassidim took it for granted that he was going to be, many of them understood these ambiguous statements in that light. And perhaps he did mean it that way; after all, just as it was reasonable for his chassidim to expect him to be moshiach, it was reasonable for him to have the same expectation.
And who is to say that it was wrong? It is very possible, even likely, that had we merited the geulah during his life he would have been the one to bring it. However, that didn’t happen. Whether he thought it would is now irrelevant. We should now expect moshiach to be someone who is currently alive in the same physical sense as all normal living people.
However, if he comes back to life before the geulah, as certain tzadikim will, then it will once again become possible for him to be moshiach. It’s not likely, but it could happen, and if it did it would not contradict the Rambam. So it’s not wrong for those who wish desperately to hold on to that hope, to do so. If it encourages them in their shmiras hamitzvos it’s a good thing. So long as when the real moshiach finally does come, and it’s not him, they will accept him. (The same goes in reverse; if it does turn out to be him after all, the rest of us will need to accept him.)