True, but some members here will tell you that once a tank is cycled, established, and has been running for some time (not quite sure how long on that), that the majority of the BB colony will colonize in the substrate, and other areas of the tank, rather than in just the filter (media) itself.Surely you have that wrong way around..?
Washing media in unconditioned tap water WILL kill ALL bacteria...that's the whole purpose of chlorine/chloramine in our drinking water!
Washing media in tank water will do no such thing.
So theoretically, one could wash their media in chlorinated tap water, with no ill effect on the cycle.
I suppose that is up to debate, but I tend to err on the side of caution, and only rinse my media in old tank water.