That's what I do. It works well until you start stalling.
Actually, a better example from personal experience. Deadlifts are a back exercise and hits the hammy pretty good. When you get into higher weights on the deadlift, running the next day is different for lack of a better term. You really feel the soreness in those particular the back and hammy.
I really think that it is when you get into heavier weights that running is something to hold off on. If you can do a 5K, run once a week to keep the 5K ability there. I run once or twice a week now but i want to increase it.
Bottom line is that if you are truly taxing your back and hammy like in my case, you might want to run less so there is some recovery time.
And one more thing. I defer to whatever SociallyChallenged says. I jsut think the no running thing is kinda silly. I do eventually want ot do rowing for cardio though.