follow up every single allegation?
OMG Joe Blow has a picture of something obviously legal on his Facebook! Go sick’em!
But, yes, they are required by law in many jurisdictions to follow up on any complaint. You haven't lived until that BS has been aimed at you.
BTW, if the Social Workers think they need more caseload, they will lie to take a run at you. If you find yourself in that position, get a lawyer with teeth and don't talk to the Social Serpents. Anything you say will be distorted to look like a violation of the rules they seem to make up as they go along. Those rules are highly subjective, and the wisp of a rumor is treated by them as Gospel.