Think about if you isolate your bicep for curls. If you do alot of reps there is going to be alot of blood flow to that area. Same thing in if you pump your arms faster more blood is going to be directed there. This is definitly a touchy sort of topic, but I do believe it that if you work a muscle group more blood is going to be directed there.
Also I dont think doing sprints after a game is really going to affect how your arm is going to feel. If anything it might take stress off of it because sprinting is natural motion and throwing is not. I'm not saying pump your arms like a wild man, just do sprints and pump your arms naturally.
This is what I have always found worked best for me. My arm just always feels better after sprinting in general. I also have tested this on my self. For 2 weeks I did long distance after games, and the other 2 weeks of the month I did sprints after games. My arm always felt better the next day after sprints. Now I know its not a long study and its just me, but it has always helped my recovery to do sprints.