One other thing to think of is that they could change the class-skills around when you switch to a different job. Take a look at the ACN trio. Based on which Job you are in, their summons change accordingly but still use the same ability slot. Whose to say that they couldn't change multiple abilities for different jobs?

I.e.
Fast Blade for GLA/PLD stays same.

for DRK: remove enmity bonus, increase potency.