The charge of "false arrest" is a scare tactic, to make you rethink your actions, so they can avoid their job, but if your are making a lawful arrest, then false arrest won't stick.
And what you described would be false arrest when someone decided to set you up.
I've had the misfortune of having to put the cuffs on people who said "CITZEN'S ARREST!" without making sure that they were 100% correct, because the law doesn't give a damn as to whether you THOUGHT you could make an arrest.