Nope, no truth to it whatsoever. Exercise, vigourous or light, does not affect the amount or composition of milk that your body produces. The only reason I can think of is maybe because you're tired after exercising and breastfeeding when you're tired could be a wee bit uncomfortable. But that's just my supposition and no scientific reason for that.
This is nonsense; it is perfectly safe to breastfeed after you have exercised.