Actually the study says that riding to work is more likely to result in the recommended amount of exercise to gain these health benefits. It is the amount of exercise, not the fact that the exercise comes from cycling.
Conclusions Cycle commuting was associated with a lower risk of CVD, cancer, and all cause mortality. Walking commuting was associated with a lower risk of CVD independent of major measured confounding factors. Initiatives to encourage and support active commuting could reduce risk of death and the burden of important chronic conditions.
Sounds like the usual example of how physicians should not do statistics. It's probably more likely that cycling to work is an indicator for healthy behaviors such as a good diet, not smoking or drinking to excess. I haven't seen the study, but to say that just riding your bike to work 30 miles a week greatly lowers the risk of cancer is probably not accurate.
Doubtful as I am, I hope its true because I've been bike commuting for 24 years.