You'd think that, but in most cases, you'd be wrong. The President of my IDPA club works for a congresscritter. SHE has been in the immediate presence of Governor Jeb Bush, except then he wasn't the Gov yet, but he was a son to a sitting President and surrounded by Secret Service. She was carrying a Glock 21 45 (no mouse gun!) in a special concealed compartment in her purse and they never caught on. I have carried concealed many times in the presence of federal agents and street cops and not gotten a second glance, and I was paying discrete attention to them! Face it, 99.9% of the population are not that observant.
While you're absolutely right that it wouldn't be caught most of the time, it only takes one moment of reaching the wrong way or turning the wrong way to reveal yourself. Someone might get away with it 99 times and get nailed on the 100th time. They might never get caught, but it stands to reason that some will probably get caught carrying concealed weapons in violation of the policy.