There is absolutely nothing to stop this, nor is there any need to, as one airline's PNR will only be valid in its own systems. If airlines have pooled PNRs then they create their own rules among themselves for how to stop it.

This explains why when you have a BA/AA mixed booking you end up with two PNRs, one in each system - as AA might already have issued the same one to someone else. Most airlines have a time frame in which PNRs won't be reused (usually 12 or 15 months). I think a FT game should be to see if anyone's ever had the same PNR twice for different (unrelated) bookings...

It does occasionally happen that an airline looks up a PNR a customer gives them and it's the totally wrong booking relating to another airline. Funny to watch as an outsider, less so as a participant (either side!)

Individual passenger records are identified by ticket numbers - or, more specifically, a Prime ticket number (in case more than one ticket is needed, e.g. if you have more than four coupons). This ticket number will begin with an airline code (e.g. 125- for BA, 001- for AA) and will be unique. If it's held in Amadeus/similar then other airlines can access it - and when they do, that's when they issue their own record locator (PNR) for it.