As far as your request for "input," what difference does it make if someone else "was fired and re-hired"? You wrote that some "lawyer suggested . . . that if [you] could find another person who was eliminated for the same reason and re-hired [you'd] have precedence [sic] to be considered for re-employment." That's just plain silly unless you are/were a civil service employee or a member of a labor union that has a collective bargaining agreement with your former employer. Unless one of those things is true, "precedent" is meaningless.
Beyond that, we have no conceivable way of knowing (1) if phone calls that some private investigator might make to people we don't know will or won't "alert" the company to the inquiry; or (2) if anyone currently employed by the company will reach a conclusion that you're the one seeking the info (or any other conclusion). As for the investigator being "required to give the firm the name of the person who hired" him/her, no such legal requirement exists, but it might be that someone might be willing to give out certain information only if the PI identifies his/her employer.
My guess is that you're only continuing with these inquiries to see how long folks here will continue to waste their time with you. As for me, I'll now be adding you to the list of folks whose posts I block.