If nothing else, contact a mobile technician to take a look at your roof. Even if he does a full recaulking job, you"ll still have many hundreds of $$ in your pocket. Now, if the problem is actually delamination of the rubber roof from the substrate, you might be in for some serious repairs. I've recaulked my roof areas several times since we've owned it and it's not that big of a deal. The Dicor self-leveling caulk flows on over the old (that's been cleaned). I like to use a plastic spatula to smooth it nicely before it starts to skin.
If they want to peel the old caulk from the rubber roof, they risk tearing the roof membrane. Dicor does not recommend peeling the old caulk off.