Bizarre Bottom Bracket Baffles Bad Bicyclist

Blliteration aside,

Are bottom brackets self-centering? I've got a 68mm BB (110mm spindle)
that seems to be off-center on my '02 MTB (with 68mm BB shell). I
think I have installed it correctly...the fixed cup (DS) is screwed in
as far as it can go, such that the flange is pressing against the side
of the BB shell. The free cup is inserted as far as it can go (with a
couple of threads showing). The BB is square taper.

The gap between crankarm and chainstay is larger on the NDS by about
2-5mm. I swapped the crankarms and placed them in various positions on
the spindle to rule them out as a source of the problem...in all cases,
the gap was larger on the non-drive side.

Assuming the frame is symmetrical (it appears to be, and is in good
condition), is this kind of discrepancy acceptable/expected? Have I
installed the BB wrong? Am I doing something else wrong?

Thoughts are appreciated,
Dave