Google "sawdust transmission used car." Fouled lube can make a difference in some cases. Not gonna pick sides for this particular case, all I'm saying is it CAN make a difference. Maybe the shop guy is a man-splainer OR... maybe was just trying to make some interesting conversation.

Also can I just say, chain is awesome. Its such a wonderful way to transmit power. Driveshafts gears hydro pumps and rubber belts not nearly as good a way. A good chain hardly will ever fail or need fussing over. And inexpensive to replace most times. I love chain.