I've invested 16M in medical, and have a player out for 11 days with a strained neck. At time of injury he lost 1 point of power, nothing else. He doesn't need a 15-day DL stint, but will it aid his recovery to be on the DL, as opposed to just resting him? In other words, does my medical budget help all injuries or does it just help players who are on the DL? This is one of those critical questions that will help me deal with future DL decisions and future budgets. Thank you.

Medical is instrumental in reducing the time of the injury. Had you had 10m in medical, he may have been out 30 days. If he is not DL'd, he won't get a recovery bump(they are not guaranteed anyway).

i've been told that putting someone on the DL doesn't affect his recovery.

There is a recovery cycle that you won't see if he's not DL'd. That makes some people happy. But, as I said, there's no guarantee that skills will be recovered on that cycle. That does not make people happy.