Originally Posted by DanniNX

In my opinion a real professional should not offer to do anything but a top quality paintjob (I don't). Paint that peels is just not a pro paintjob. As for clearcoat, the color on most modern cars will require 2coat painting, those that don't are solid colors like plain red with no silver effect or anything of that sort (those colors will still look better with clearcoat).
I would never trust a company that offers paintjobs that they admit will peel off.

Here's a list of things that should be done... (this does not account for rust)
Entire car must be sanded prior to primering
The car should get a coat of epoxy primer followed by at least two coats of filler
The filler should then be sanded and the car painted, preferably with a 2coat system (basecoat+clearcoat)
The car should then be baked for 30 minutes or left to harden over night.

Here are the possible reasons for paint peeling...
Car was not sanded prior to primering.
Car was not primered at all and not sanded before painting.
Incorrect combination of primer, basecoat and clearcoat was used.
Too long time passed between filler being sanded and the car being painted.
Too long time passed between basecoat and clearcost (resulting in only clearcoat peeling).

I hope this gives you some idea as to how to judge a paintjob. Now you can go ask them how their process is.