Accepted knowledge in these communities and with most trainers is recovery days are when the body grows.
Yes, but not by necessity. The days following a bout of resistance training are when muscular growth occurs. Most people don't train the same muscle group multiple days in a row, so as a result of their scheduling, the growth is happening when the muscle is being rested. But that doesn't mean that muscle growth can only occur at rest.
While there is evidence that excessive training volumes are detrimental to muscle growth, there is no evidence to suggest that training during the muscle growth period interrupts muscle growth. So, consider the following three training programs:
- You do pushups twice per week, doing seven sets to failure per session, for a total of 14 sets per week.
- You do pushups every day, doing two sets to failure per session, for a total of 14 sets per week.
- You do pushups every day, doing seven sets to failure per session, for a total of 49 sets per week.
Training programs 1 and 2 have the same volume, so there's no reason to believe that program 2 would give worse results, even though it has no rest days. Training program 3 also has no rest days, but it has drastically excessive volume, and so could result in reduced performance and increased injury risk.
And that sans recovery days you're only breaking down muscle fibers without letting them grow back, eventually leading to negative results.
You don't damage all of your muscle fibers in a training session, and you don't use 100% of your muscle fibers when a muscle contracts, so the body still has plenty to work with and isn't likely to re-damage the same muscle fibers again.