This is one of the most annoying and awkward pieces of 3.x rules
You don’t get enhancement bonuses to AC, you get enhancement bonuses to armor bonuses
So, armors grant an armor bonus to AC. Seems simple enough.
Then we have enhancement bonuses. You could, in theory, have an enhancement bonus to AC; if you did, it would stack with an armor bonus, since they are different bonuses. However, as far as I know, there is no effect in the system that gives a creature an enhancement bonus to AC.
No, instead enhancement bonuses are applied to items. When you wear magically-enhanced armor, you don’t have an enhancement bonus, the armor has an enhancement bonus – to the armor bonus that it gives you. So in short, your AC doesn’t “see” an enhancement bonus at all; it just sees a (larger) armor bonus.
A similar example exists in the amulet of natural armor’s “enhancement bonus to your natural armor bonus.” This time, the enhancement is on the person wearing the amulet, but it’s not an enhancement bonus to his AC, but an enhancement bonus to his natural armor bonus. As far as the wearer’s AC is concerned, it sees no enhancement bonus, just a larger natural armor bonus.
And so it is with magic vestment: it applies an enhancement bonus to an item’s armor bonus (including an armor bonus of +0 from a non-armor). Your AC still only sees a larger armor bonus, not any enhancement bonus.
Thus you might have a shirt that has a base armor bonus of +0, to which it receives a +4 enhancement bonus. The wearer of that shirt gets a +4 armor bonus. If they are already wearing full-plate, the +8 armor bonus of that supersedes the +4 armor bonus of the shirt, so the shirt becomes pointless. On the other hand, magic vestment could be cast on the full-plate, giving it a +4 enhancement bonus, improving its armor bonus to +12. If it had instead been a +1 full-plate, the +4 enhancement bonus would supersede, not stack with, the +1 enhancement bonus, so the armor bonus to the wearer’s AC would still be +12.