Parasites cannot breed without a host, which is part of being a parasite, so the concept does not hold water. Many folks believe (incorrectly) that nematodes, flatworms, various 'pods, snails, and such that develop significant numbers in tanks with high-organic substrates (as untended substrates are prone to go) are parasites. They are not. But it is a case of too little information and unfounded conclusions.
Certainly large numbers of unintended inverts developing in a tank is not desirable, but correcting the situation which allowed the beasties to develop is just a matter of improved upkeep and water quality. And certainly fish in such a tank may be more succeptable to parasites (due to water quality issues), but the parasites were not generated in the substrate. Spontaneous generation is a non-starter, as is multiplication of parasites without hosts.