Here's a good "for instance".
Suppose a site-visitor owned a nice gun -- an older Colt Python -- that was stolen in the last...oh, 3-6 months. The burglary was reported, but he didn't have the serial number. Then, lo and behold, Mark B. posts a photo of a Python he says he picked up in '75 from a neighbor when he lived in another state. Our unscrupulous site-visitor copies down the serial number and then provides that to the police as his own. He waits a month or two and then calls the police because he "happened" to stumble across the photo of "his" gun on the internet.
Now you have some selfish, dishonest jerkwad getting the police involved in tracking down the person. That might involve TFL having to provide data and certainly the guy's email provider will have to do that. Then some poor TFL member is watching the Saturday college hoops when cops show up at his door asking to see his "stolen" Python serial number 123456 ... it gets uglier from there.
This is one reason I usually mask or blur the s/n on photos of my guns. Masking is a bit more certain. And I have receipts for all of my firearms too. Should someone attempt such a scam on me, I'd certainly press charges in response, once I showed my receipt to the PD. After that, I'd sue his butt big time.