Hmm, this is a tough one without actually having the thing in front of me.
First off, what kind of frame is it? If it's a carbon frame with a metal BB shell insert then yes, you're right in being hesitant to just torque on the thing. Best to take a more gentle approach here, which can include penetrating oil, mild heat, etc.
Secondly, do you remember how you installed it? Did you grease the threads or apply threadlock? And even if so, do you wash your bike with any frequency or ride in the wet? Either can break down the grease in the threads and cause corrosion, in which case... see above regarding oil and heat.
If it's not a bonded/molded-in shell insert, sometimes you do just have to apply a lot of torque to break it loose. BUT, if you do use a lot of force and it starts to move but it doesn't get any easier (or worse, if it gets harder), you might be tearing the threads out of the shell along with your cup.
In any case, experience is your best friend here as a good mechanic (with emphasis on 'good') will quickly be able to evaluate the situation and decide which approach is best - I've personally seen this situation go a lot of different ways, and not all of them good. If you're not comfortable tackling this on your own or just don't think you've done enough wrenching to know, better to pay someone their requested fee to get it done properly.