IMHO it is absolutely unheard of that a boarder in a private barn would install a camera without complete prior permission and cooperation of the Barn Manager. In typical boarding barns, horses can change stalls and paddocks frequently at the decision of the manager. Boarders don’t get to install permanent personal fixtures of any kind and typically don’t even get a choice in buckets or hay nets.
This is completely different from the Barn Manager installing official security cameras which typically focus on entrances and exits and parking lots, to provide evidence in case of theft or vandalism overnight.
If a horse really needed a stall cam, like Mare Stare for a pregnant mare, that should be set up to not capture common areas like the aisle.
It is very possible that the boarder in question is bluffing, and if the camera is very well “hidden” it may not exist.
As far as things going up on social media, I could imagine some people doing that and others not. It really depends on the toxicity and perhaps youth and impulsiveness of the individual with the camera, whether they would think it useful or amusing to post unflattering candid shots of other boarders and barn workers scratching their butts or knocking over wheel barrows or “borrowing” fly spray.