Your understanding is COMPLETELY WRONG.
I have done mine twice in the last 3 years, once after I bought it used (wanted to start off 'clean'), and then this last spring when it changed all fluids to synthetic, including the trans fluid. Especially the last time, the change was noticable in terms of smooth and crisp shifts.
It is not hard to understand why a power flush is better. By simply draining the fluid, you get only about 50-70% of the fluid out of the tranny itself. You sure don't g3et the fluid in the torque converter (yes, you cen take the drain plug off the converter, but how many go through that step), and if you have the tranny fluid cooler, you certainly don't get that fluid out. Plus, what about the gunk and deposits in the servos, clutches, galley pathways, etc.? In simple terms, they stay in.
To your point that they do not want to take the cover off, well they don't. Most tranny's can leak after this. Plus, the filter may not need to be changed becuase power flushing is a reverse flow process that actually cleans the filter. In my case though, I still insist on taking the cover off, replacing the filter and doing a visual on the tranny.
My advice, based on my own very good expereince is ALWAYS power flush, and go with synthetic fluids. A reliable shop will use the correct fluids (there really is only two kinds for trannys). As a matter of fact, when I had my tranny power flushed, I had my brakes & power steering power flushed. In all I had synthetic fluid put into: Brakes, power steering, tranny, rear diff, front diff, transfer case. Of course, I always use synthetic motor oil. For those of you that complain about leaks with synthetics....I have none.