Even if you aren't (unintentionally) bending the strings sidewise, I'm convinced there's still a bending problem which gets worse as you move up the neck. When you fret a note down in the first few frets, your finger easily fits between them and the string only has to make a shallow V bend. By the time you get up around frets 15-20, your finger is big enough to fill in the space. So now the string makes a fairly sharp bend over one fret, runs flat across the fingerboard mashed down by your finger, then bends sharply again over the next fret - which ends up making it stretch more than for a lower position note.
Back when I was playing guitar, trying to learn jazz and being careful not to bend notes, I started hearing things get progressively sharper as I moved up past the 12th fret or so. Learning to use a lighter, more controlled fretting technique (consistent and just enough to get a clean note without buzzing), took care of this for me. This is another good reason to do your own intonation, because if you use different finger pressure than the person who does it for you, it's not gonna be right.
Valentino - I'm not trying to suggest you have less than perfect technique, or fat fingers, or anything like that. I've also never had a fretted bass, so I don't know whether that kind of behavior is still significant, but it seems like it could be, and that you could notice it becoming less so from 32 to 36.
David - you're right (you knew that) that both the general stiffness of the string (its design) and the additional problem of stiffness at the ends, possibly aggravated by a large break angle, can make the string behave as if it's shorter than it is, which could make those upper notes sound sharp. Again, I don't know what to say about fretted basses, but my sense is that at least on the scale of a regular guitar, bending would have a more significant effect than stiffness (I might be wrong).
I don't have to worry about frets, but I still think about end stiffness a lot, because of how it skews the harmonics. It bothers me a bit that there's so much variation in bridge-tailpiece spacing among different Alembics - they can't all be right. I even had a couple of ideas for an adjustable height tailpiece so I could minimize the break, but shelved that because there were too many other things going on with my custom (both time and money).
Oops, none of that really has much to do with the low end sound - but it's still interesting...