Fact or misinformation?

Dave is entirely correct. There is one instance that might damage a stereo cartridge and that is trying to play 78s with it. The groove size is much larger and a modern cartridge will bottom out in the groove encountering more friction than usual as the point digs into the shellac. 

I do not bother with mono cartridges. A stereo cartridge will play mono records just fine. Imaging is not important as there is no image. Mono records actually sound best off axis.

How can it possibly make any difference whatsoever if both sides of the groove are identical (mono) or different (stereo)?

Obviously a salesperson with zero in-depth knowledge making ill-informed guesses.

Thanks for the laugh!

NO! 

@intactaudio +1

No...in fact a mono record can sound quite good played with a stereo cartridge. Especially if you engage the mono switch on preamp if equipped. You can buy an in line mono/stereo switch. I opted to go the mono cartridge route, Grado, as I have a removable headshell for easy cartridge swaps. Keep in mind though, mono cartridges/stylus should only be used on older true mono records....the later "dubbed" mono records can be played with stereo cartridges as the grooves were cut in the same manner as their counterpart stereo versions. The grooves on the older mono records were cut differently with wider grooves.