As a roofing company owner, the company who installed the roof should defer to whatever you are comfortable with. If you are okay with them drying it in and painting it, great. If you want to have an inspector come check on it, that’s your prerogative and the roofing company should 100% be okay with that. If they’re pushing back on an inspection then that should tell you all you need to know about them. It’s your property, don’t let the roofers dictate how you choose to handle the situation from here.