Discussing whether Reb Aharon or The Satmer rov could be the moshiach, meirs asserted that they could not because “they do not fit the Rambam’s criteria of who Moshiach is”. MDG replied that the Lubavitcher Rebbe doesn’t either, and meirs insists that he, unlike them, does.
The truth depends on what you mean by “fit the criteria”. The Rambam gives very few criteria for who could be the moshiach, and based on those criteria all three qualify. The Rambam’s main point is to give criteria for how we will know when someone is the moshiach. He says we will know the moshiach by his actions, and gives two sets of tasks that he holds the moshiach will perform; if someone has performed the first set then we can assume he probably is the moshiach, pending his completion of the second set.
If this is what you’re referring to, then none of the three performed even the first set, let alone the second. The Lubavitcher Rebbe did certain things that could be seen as symbolically foreshadowing the tasks that the moshiach will perform. Had he then gone on to perform those tasks themselves (or if he ever does perform them) then those earlier actions would be seen in hindsight as a beginning, much like the symbolic actions the nevi’im used to take, to signify later realities. If one were to analyze the lives of the other two the same way, one might well find some or all of the same tasks foreshadowed somehow in their lives too. None of it means anything unless it eventually leads to the reality. If one of the three comes back and does the tasks themselves then they will be the moshiach.