This just happened to me as well.
I've had Get Famous for about a month now, and I've played other celebrities prior to this one. But this is the first time I have seen this bug.
My current Sim had just ranked up to Proper Celebrity, though, he'd had a Stan for quite a while. But it was only after hosting a meet-and-greet on a community lot that he got a text message from a friend stating that "I heard you like to steal things...."
I do not use mods or CC; my Sim does not have the Kleptomaniac trait, and has never stolen anything. But I can confirm that this is not related to the Stan quirk.
I purchased Quirk-B-Gone from the rewards shop and got rid of the Stan that way. A few minutes later, he gets a second text from a friend with the same message. If this continues, his reputation will be completely obliterated, and I've worked so hard to keep him out of trouble.
I hated the false accusations in TS3, and was just starting to warm up to the fame system in 4 when this happened. I wonder if there's any hope left for this save, or if I should just cut my losses and start over.
Product: The Sims 4
Platform:PC
Which language are you playing the game in? English
How often does the bug occur? Happened twice in the past 5 minutes, but that's it so far.
What is your current game version number? 1.48.94.1020
What expansions, game packs, and stuff packs do you have installed?
EPs: All but Seasons and Cats & Dogs.
GPs: Spa Day, Outdoor Retreat, Jungle Adventure, Parenthood
SP: Luxury Party, Vintage Glamour
Have you installed any customization with the game, e.g. Custom Content or Mods? No
Did this issue appear after a specific patch or change you made to your system? No