You're assuming an awful lot from a very brief description of what happened.
"As previously said, all the info he got from Facebook could probably have been given by the waitress. Or by the local phone directory for that matter."
Only he didn't - she "was able to give Leary the name of her fleet-footed acquaintance, and he immediately ran it through Facebook." If the perp didn't know if she was working or not it suggests they didn't know each other too well, so she might not have been able to offer up any further info.
"No it did not, because he still relies on his and his staff's belief that the guy and girl were really there and really dodged the bill"
WTF does that mean? The crime was committed, there's no question about this! What, is he going to make it up?
"it still boils down to his and his staff testimony. He used FB only as a directory. He also got the employment place, which allowed him to indulge on some vigilante-like justice (which is NOT a good thing in theory, even if it appears to be justified here it's certainly not proportionate, at least if the firing had this story for only reason)."
Again, WTF? Is your name Rumpole of the Bailey or something?
A group of guys evade paying for a meal by legging it from the restaurant.
Manager employs bit of memory and logic (hey! the IT angle), tracks down one of the perps who fesses up, pays up and gets sacked by his employer.
End of story.