I've seen discussions on this before. Unfortunately, it's urban legend.
The founding member of Dream Theater (John Petrucci, John Myung and Mike Portnoy) attended Berklee College of Music in Boston. We've never had a chapter there. The logo was designed by Charlie Dominici, who was with DT for a shorth period of time; I don't know if he went to college. Bottom line: none of these guys are in the alumni database.
The Majesity symbol was supposedly modeled after a monogram or cipher of Mary, Queen of Scots. Presumably, it was the one used in her capacity as queen consort of France:
and not the one used as Queen of Scots:
There is no doubt, though, that the Majesty symbol suggests the letters Φ, Μ and Α:
This is especially the case when you compare the logo to the old monogram used by Sinfonia:
An interesting coincidence, but it would appear that's all it is.