I believe there is anecdotal evidence that suggests that strenuous excersise and not enough calories in, can impact supply. Breastfeeding uses up a lot of energy in calories, so you need to make sure you are eating enough to sustain the bf and any excercise you may do.

But if you are eating a plentiful well balanced diet (I think the ABA recommend at least 3700kj?) you can then top up with healthy snacks and do some gentle excercise?

Each to their own, of course. I was swimming and bushwalking from when Charlie was only 2 weeks old in the middle of an Adelaide winter: it did me the world of good, physically and mentally! (And he came to no harm at all, nor did my milk supply.......)