There are aerobic bacteria that require oxygen, anaerobic bacteria that live in an evironment without oxygen and facultative bacteria that don't seem to mind in either situation. There are also spore forming bacteria that can go into a resistant spore phase in adverse circumstances. Adaptable little critters eh?
What worries me with those claims is that getting rid of the "crud" probably puts it into solution and therefore increases nutrients, and getting rid of nitrate to nitrogen would mean the completion of the nitrogen cycle to nitrite then ammonia then nitrogen which would not be good for your fish.
I may be wrong but it sounds too good to me to be true---unless I have missed the point here.