Both the lens and the camera can be adjusted, but only Canon can adjust the lens, while those with AFMA in their body can adjust that body for a particular lens.
You can send your 60D and lens to Canon, and they can adjust both of them to specification. I had my 35mmL adjusted at Canon Irvine, and now it is right on for all my camera bodies.
Most of the time, new lenses are pretty close to perfect as received, but I have received a few that are off by enough to be detrimental to my images.
I don't recommend getting a fast f/1.4 lens for a 60D due to no AFMA, and its a particular issue for third party lenses, because Canon will not adjust them to match the body, so you must send the lens to its manufacturer and the body to Canon, and hope that fixes things.
Sigma has a new lens adjustment tool that works with their new high end lens models, so that should help if you pick one with owner adjustment capability. In that case, the adjustment is in the lens. The drawback is that the lens may need different adjustments on different bodies, so its not a ultimate solution.