NONE of which guarantees you a rehire, or grants you any kind of legal recourse if you don't get one.
Why is the consensus not use a private investigator?
I really need to get that job back.
Because it doesn't matter a bit if they have rehired someone else back that was previously terminated. Even if they did it doesn't mean they have to hire YOU back.
You won't get that job back. Ever. Not under any circumstances. Period.
If you use a private investigator, it will cost you money which you also won't get back. It will seriously irritate your former employer, to the point where the police are called and harassment charges will be laid against you. And your chances of prevailing over your former employer when you're dragged into court about your harassing behaviour are exactly nil.
So not only will you not get your job back, you will also wind up with a criminal record. This is not a millstone you want around your neck when you finally start looking for work elsewhere.
(And please keep in mind that your former employer is legally free to tell anyone who asks about your harassing behaviour. If you do manage to get close to obtaining a job offer from another employer and that other employer calls your former employer for a reference, all your former employer has to say is "well we not only had to fire him but then he harassed us so much we seriously considered calling the police on him" and you can kiss that job offer good-bye.
Let's say your private investigator determined that there was someone who was fired under the exact same circumstances as you without any variation whatsoever. That person did A, B and C and was hired back. Okay, there's your precedent. So you do A, B and C.
You know how much legal obligation that precedent means with regards to hiring you back?
Zip. There is NO legal obligation on the part of the employer to hire you back, even WITH precedent. None. Zero. Negative. Nyet. Nada.
How much time and money are you prepared to put into a losing proposition?
Agreed with the other answers. If there was a betting site that I could bet $100 that the OP will fail and fail big time on this pursuit, I would take that bet, as would likely almost ever other poster.
Could there be a court decision going the other way? Sure. So what. There are a lot of court decisions, and if one of them says "up is down" but all the rest of them say "no, down is down, dummy", guess which way the next court decision will almost certainly go.
I can remember when occasionally the court would issue a decision that severance pay was not subject to FICA/FUTA taxes, my bosses wanted to immediately file for refunds and start changing who we handled things, and I very strongly argued to wait for the appeals to work out. I put this in writing and copied Very Senior Management, who pissed and moaned but held back until IRS did indeed win on appeal (over and over again). There are always out lying court decisions, but these decisions rarely last through appeals.
The OP is talking about no supporting court decision at all. Just the possibility that some employer at some time in the history of the world might have rehired someone with sort of similar facts. Maybe Agamemnon being forced to rehire Achilles. This is not precedence. This is a best very wishful thinking. This is at worst "get a psych evaluation now" territory when someone cannot judge fact from fiction. The OP has better chance of being elected the next President of the USA then they do forcing their prior employer to rehire them. There are very, very few legal precedence for the employer being forced to rehire an employee. Even if a wrongful termination could be proved, and the OP has said nothing supporting this action, at best there would be monetary damages, not a forced rehire.
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.
And here's something else for you to consider.
For the sake of argument, let's suppose that you find some Very High Priced Lawyer who hires a Very Expensive Investigator and finds a set of facts that convinces the employer (wrongly, because no such set of facts exists outside the exceptions that have already been indicated) that they are obligated to hire you back. Hey, great, you won!
Now, the company has been forced, very much against their will, to bring you back. You think they're going to be happy about that? You think all will be smooth sailing after that?
Think again. That code of conduct you've been so concerned about? Better make sure you follow it religiously every hour of the day.
Due on the job at 9:00? Better hope that the overturned tractor trailer on the road ahead of you doesn't keep you there too long, because at 9:01, you're late and can be fired for it.
Sick with the flu before you've been there long enough to qualify for FMLA? Even WITH a doctor's note, they're free to let you go for missing work.
Computer down and you submit a report a day late? Not performing to standard, don't slam the door on the way out.
Are you getting the picture here?