A lot of athletes got massages done back then and still do, foam roller is just a way to give yourself a bit of a massage, nothing new there.
You can't be serious, so an animals/person's life is in danger and you expect it to stretch before moving?? This is up there with one of the dumbest things I have read in a long time.
There is a flight or fight response that injects adrenaline into your system that makes you move and not feel pain. Then once the situation is over the body will deal with the injury pain caused by the sudden movement. I remember braking my foot in a full contact kick boxing match, was about half way through the second round, I finished the fight as I felt no pain till about three hours after the fight, went to hospital and was told I had a really bad beak in my right foot, I do remember when it happened but did not think it was broken as I felt no pain during the whole match. It's just what your body does.
Have you ever noticed that pretty much all animals will stretch extensively after a rest and before activity, I even seen our cat get up have a stretching session and lay back down to keep sleeping. If it gets up is will stretch extensively before moving off, bigger cats and dogs do the same thing.