The best I could find was a 2005 study which focused on older adults. They haven't identified the actual components causing the associations, but the relationship is there:
Thus, the data are
consistent with the notion that exercise may facilitate wound healing,
in part, via neuroendocrine regulation.
There's the elaborate mix of hormones of course, but some of the ideas postulated are actually rather straight forward:
Also, exercise may contribute to blood flow to the skin and increased
skin oxygen tension, thereby enhancing woundhealing rates.
That study of course looked at wound healing, but it doesn't seem like much of a stretch to imagine that the same factors aiding (and detracting) from wound healing would be in play with an injured muscle.
Not directly answering your question, but germane to it, is also the idea that people who are athletic generally pay more attention to their diet, have better physical awareness, and probably are doing better in areas like hydration. They're also less likely to be suffering chronic health conditions, which in turn decreases their chances for complications from injury and illness.