DeePee, I believe anyone who understands athletic performance in pitchers requires a healthy body that includes endurance and cardiovascular fitness. There are many ways to achieve this other than long distance running. I think that is the point some people are making. You have to run in baseball (D'Oh) but at least from my perspective there is a lot more knowledge today in training athletes for baseball than there was even 4 years ago. I for one would not be looking to a travel ball coach for this advice, just the same as I would not look to a pitching instructor for a workout. (unless they were highly trained in this area and most if not all pitching instructors are not). Guys like P3sports, Eric Cressey, Gymjones, who specialize in fitness training for athletes (including baseball) are where I would look.
As an example my son, a college pitcher, is in extremely good cardio and strength shape, he can run a 5'30" mile if required but does not run very often. Much of the cardio gains are achieved in interval training as well as bikes, rowers, and "ski rowers" If you have not look at the above sites I would if I were you.
Good luck.
BOF is right on. You dont go to a pitching coach for training unless that coach has been trained to give that advice.
ML pitchers with big contracts dont do very much in spring training. Its a very long season and they need their knees to hold up so running is minimal. 40 man roster guys not on the 25 man and invites will do all they can to get noticed. Running still is a requirement in college and milb pre season, I think its more of a mental thing than actual physical and you can achieve cardio fitness in many more ways than pounding the pavement.
Usually the guys who have been to college catch on much quicker than those that have never been through serious training for their position.