College Dispensation isn't just us grabbing Dragomas and having the same conversation with the Emperor we'd have had anyway, it's -as you said - Dragomas relying on delegated authority, and Dragomas' authority is lesser than the Emperor's. The Emperor going out of his way to personally say "Yes, this thing you're doing is fine, go for it buckaroo" is more bulletproof than Dragomas doing so, especially when having Dragomas do so involves telling more people where to shoot their bullets.
I understand arguments that it shouldn't matter; I understand arguments that it won't matter. I even understand the argument that however little influence through Heidi this will cost us would be better spent elsewhere, though I personally prefer spending a pittance on preventative measures over calling in favors to deal with consequences.
But I do not get where the insistence that the personal backing of the Emperor is somehow not the strongest guarantee we can get is coming from.