The underlying question to me on fitting is... if one pays for a fitting, first time or not, will they *learn* something worth the cost?
The question of fitting only arises when one thinks that the current fit is wrong. If the bike feels great, we're not having this discussion. Then, the conversation boils down to one of two general opinions: you can figure this out yourself or it's valuable to get some guidance. Just depends on how, and how fast, you want to learn more about body/bike interface. Key point here: learning. You can learn this yourself, or you can get a lesson. Plenty of threads around here to learn a solo approach to calibrating bike fit. If you decide that a professional fitting is the best way for you to learn what you want to know, then go find a fitter who is going to teach you something, not just spin the hex wrenches and send you off -- almost everyone agrees that to be a waste.
To your original question - IF one chooses a professional fitting, then one should learn enough to understand what to adjust in the future. Else you didn't get your full money's worth.