Ive been offeted a position with a major financial institution. My references... prior employment and criminal checks have come back good.
Only thing keeping me from being accepted for the final offer is a few years back I was a teller. I was fresh out of school and relied on public transport.
That winter was very very bad which delayed my commute a lot. They also placed me at a branch 20 miles from home which didn't help.
Well, I ended up being let go. The branch manager made it clear it was due to the latenesses and even said, "at the interview i was actually worried about the distance."

Well, this prospective employer needs a written statement from them as to why I was let go.
In Pennsylvania, by law, they are not to give this info out.
I spoke to both my ex district mgr and HR and they both confirmed this.

The prospective employer is in NJ.

This is the law. And they are not willing to break it.
Can my new employer seriously rescind the job offer because they will not be able to get this info?

I mean, I begged them to please tell them but they refused.
Oh, and when I was terminated, I remember the branch mgr getting mad at me because I didn't get upset! I had my hairdressing license previously and nicely said that I will return to the salon.
He then apparently changed the reason for termination from attendance to misconduct!! I was a very good employee, made my sales and followed the rules to a T.
They realigned branches, laid off good people, half the branch quit because they were so disgusted, but I stayed loyal and worked hard and helped cover shifts. And this is what he does?
Can he even do that?

Anyway, my only concern is again, can I lose this position for the sheer fact that LAW won't allow my reason for termination to be released?

Thank you

This is very unusual. Most employers know that former employers will NOT put termination cause in writing - especially to a third party.

Also, it is probably not "the law" that says, simply, "employers may not give reason why an employee was terminated". Exactly what PA law says that?

Bottom line is that if an employer does not want you, move on. Depending on how long (you did not say) it was that you left that job in PA, you may consider leaving it off your resume, or state the reason that you left them in a different way.

I normally would not have put it on my resume but I signed a consent form in my application that stated they use a database called myworknumber and using my ssn they will have full view of every employer I had who reported my wages to the IRS. I just really need this position. The pay and benefits are wonderful.

Ask your former employee to give YOU (not the new company) a copy of your final termination paper work, that included cause for discharge.
They may (and I believe must) provide you copies of your file.

Then you can provide that information to them.