That's super flawed logic. People didn't recover from injuries in the past, couldn't train as hard or as often, died or lost limbs because of minor injuries due to things like infection...
You can say more research is needed to determine just how efficacious modern methods are, but you are underestimating just how much research has already been done on these sorts of things.
The body's natural healing processes are aided by all sorts of drugs, synthetic and natural. Reducing inflammation has been shown in many many studios to be very beneficial in recovering from injuries.