I think the problem has three facets.
First of all, based on what I see at the range, there are a LOT of shooters out there who can't shoot anything that could respectably be called a group at any distance. I've seen folks at the local ranges using laser sights to shoot groups that don't all stay inside the lines on a human-sized silhouette at 5 yards.
It's understandable that when one member states that they can shoot at 25 yards, groups that are better than another member knows he can shoot at 5 yards, the latter is bound to be suspicious. The first issue is that there is a truly wide skill variation in people's ability to shoot handguns.
Second, when most shooters come back from the range they only bring back or save the targets with results they like, and after awhile they don't remember all the ones that get thrown away. They only post about/brag about the ones they saved. The second issue is that there's a tendency for posters to make it sound like all their groups are as good as the one they're posting today and/or for those reading the post to make the assumption that's what the OP is claiming. For example, I've shot sub-one inch groups at 25 yards using an unrested handgun. Sounds pretty good, but the fact is that I've only managed that a couple of times in many years of shooting.
Finally, some people do make stuff up. There's a fun thread on another forum that's been running for about 3 years. A member started it by challenging all comers that he would pay them $20 for each 5 shot group shot at 15 yards using a handgun from the standing/offhand position (no rest) that was an inch or less from center-to-center if they would pay him $1 for each time they tried and failed while he watched. He still hasn't paid out.
In all fairness, he's located in a small town and the groups have to be shot in his presence to qualify. Things might have been different if he lived in a large metropolis with lots of shooting ranges and shooters. Still, the fact remains that while there are people who can shoot that well, you don't run across them every day--at least not quite as often as you read about them on the internet.
By the way, if you see someone calling another member a liar on TFL, please report the post. It's probably something that a staff member should at least take a look at.