quoted

I don't get this.  If you mean partitions defined by the classic DOS 
partition table format, then AFAICS, such a partition can start in any 
sector.

   Only at "logical cylinder boundary" (except for the first partition).

That's a requirement in ancient DOS systems that use CHS addressing 
(physical CHS, no less), isn't it  (so you can properly convert a 
within-partition address to a within-disk address)?

While I would guess most people still partition disks that way (Even 
linux-util fdisk seems to do it by default), they don't have to.

Doesn't matter for this discussion, though.  As Doug demonstrated, even 
when you do start at cylinder boundaries, half your partitions start on an 
even sector, because typical cylinders have an odd number of sectors.