[supercat]

Not too hard to understand, since oblate spheroids have flatter surfaces than spheres and so leave less room between them.

If all of the oblate spheroids were oriented identically, I would expect them to pack to the same density as spheres. The density improvement comes I would think from the fact that the oblate spheroids can be rotated to fill in the nooks and crannies. As a very crude analogy, a 13-card bridge hand is more likely to have a 4-3-3-2 distribution of suits than 4-3-3-3 even though the latter would be more "uniform".

[PAR35]

13-card bridge hand is more likely to have a 4-3-3-2 distribution of suits than 4-3-3-3

I don't think so. A 13 card bridge hand is more likely to end up with 13 cards than with 12. 4+3+3+2=12.