Our worst MU? I hope you're joking, Mewtwo has far worse MUs.
Where does he say that it's his worst? He just thinks it's a disadvantage, which judging by his justifications proves my earlier statement that if you're one of the guys who favours survivability, then of course Bowser will seem to have the edge.
A big deal was made over shadow ball, but in truth it's more than that which makes it more difficult for Bowser to approach.
The walking speed.
Bowser can't walk or move in the air for ****. Dashing is his only speedy approach, everything else is fairly easy to react to.
You can see an example in a Zangief vs. Akuma fight. The latter's walking speed and zoning make it hell for the latter to do anything since Akuma commits very little on his approaches. Even if Zangief can still crush Akuma in no time if he manages to get through, he's heavily reliant on Akuma making a big mistake for that to happen.
Obviously Mewtwo is nowhere near as oppressive as Akuma, nor is Bowser totally inept at approaching or relieving pressure. But even if the margin of error in neutral is smaller on Mewtwo's end, he still has a significant edge by virtue of his projectile and the ability to simply walk or jump away from an uncomfortable position, which IMO goes a long way to counterbalancing Mewtwo's stamina disadvantage. Maybe not enough to put it in his favour, but certainly nothing that can't be overcome with smart play.
You can't just look at Mewtwo's advantages in neutral and say he wins off of that, nor can you also say that with Bowser's weight. You have to look at the whole picture, and that picture is of two characters who can both do nasty things to one another, one of which has an easier time evading, landing hits and gimping while the other has far more bulk and raw power. In the end their strengths and weaknesses mostly cancel each other out.