I used to think that old tale was " hog wash", till the last Jeep I bought ('99 TJ) I had the tranny flushed and sure enough it started slipping.
Drop the pan, change the filter and re-fill with fresh fluid but do not let someone talk you into flushing it out.
"Flushing" at a shop usually means a high-pressure flush with a machine made for that purpose. It can knock crud loose and plug passages. Bad stuff. Stay away from it.
On the other hand, replacing
ALL the fluid can
save a slipping trans. It can't hurt it. Speaking of Jeeps, I did this 25,000 miles ago with mine, and it's been fine since. The fluid looked like old motor oil, smelled burnt, and the trans was slipping like crazy every time it got good and warmed up. Not overheated, just well warmed (like an hour of driving). When I say slipping like crazy, I mean limping it to the nearest safe place to get off the road, hardly able to get moving. Most people would have written that transmission off.
To replace all the fluid, find the cooler line that comes FROM the transmission. Cut it at a convenient location. Stick a piece of rubber hose on it to direct the fluid down into a drain pan. Have soldier B standing by to start the engine, and soldier C watching the fluid going into the drain pan. Get yourself ready with a good funnel and a couple of gallons of trans fluid. Have soldier B start the engine while you start pouring fluid into the fill tube. Keep going until solder C says the fluid is coming out nice and clean. Have soldier B shut off the engine. Use a short piece of rubber hose and a couple of clamps to repair the cut in the cooler line (it's low pressure - it will hold just fine), and then make sure your fluid level is good.
Done.
It's cheaper than a rebuild. The worst it can do is trash the trans, and if it's trashed already, what have you got to lose? It's worked for a lot of people.