Oh no, that's not at all necessarily the case. As others have pointed out, there's often a slight misalignment of the cantilever within the cartridge itself. Proper cartridge alignment aligns the cantilever to the record, and not the cartridge to the headshell.
As, lewm already indicated, that doesn't change the conclusion at all. If you align by the cantilever, then the cantilever (rather than the body) will be aligned straight in the headshell and will remain so in any arm if you use the alignment that the tonearm was designed for.