FWIW: I bought a 540i with 280,000 km. The most recent previous owner did plenty of maintenance (or more accurately fixing) while he had it, but the rest of the ownership records are non-existent. Every time I come across something that is a question mark, I have to make my own decisions about what needs replacement and what doesn't.
Personally I might have found a little less murky history if I had to go back and do it over again. When you're talking accidents, engine swaps, and other major work there are a lot of questions raised.
I didn't understand the bit about the tires ...
1998 E39 540i 6 Speed