Well, if you believe him and follow his advice your transmission will be dead in 50K miles. How much worse is it supposed to get if you change the fluid now? No need to fight with them, just walk away.
I have never heard any actual reports of Honda transmissions being damaged by fluid changes and I have no idea how that story got started. The fluid is a lubricant and lubrication is improved by fresh fluid. Note that Honda transmissions should never be flushed and that there is no user replaceable filter. When the fluid is changed only about a third of it is replaced anyway, so at 71K miles you are not terribly behind the curve. Most Honda owners will do one change (easy enough to do yourself) and run it a few days, then do a second change if the first one was way overdue. If the fluid is really old a third one is done soon afterward but yours hasn't really been let go that long.
35 years maintaining my own cars, including 9 years with my daughter's 1993 Accord (which got its first ATF change when I bought it at 167K miles and now is over 250K miles)