Just to summarize my understand if the rational basis for the mashichist position.
1. The Lubavitcher Rebbe was a leader and teacher in Klal Yisroel.
2. The Gedolim of his generation knew him.
3. There was never a concensus among all or even most of the Gedolim to denounce him as unfit to be a leader and teacher.g
4. Per the above his Talmidim have a right and obligation to follow the teachings of their Rebbe. (Also, per the above others are obligated to accord him the honor due to a leading Talmud Chacham.
5. The inference from the Bati L’Ganni speech was sufficient for the Brisker Rov to declare that the Lubavitcher Rebbe thought he was Moshiach. Such an inference is clearly not unreasonable.