Don't know where you read this but is not telling the entire story. Yes, Ammonia can be off-gassed to a point, but only under certain conditions.
This from KoiPhen:
"In water "ammonia" is in equilibrium with the ionic state "ammonium" (NH4+); the combined total of ammonia and ammonium is often referred to as Total Ammonia Nitrogen (TAN). At the pH levels typically encountered in ponds, most of the TAN is in the ammonium form, which cannot be directly off-gassed because doing so would create a steep charge imbalance. While a trivial amount of ammonia may off-gas, this is usually insignificant. In the waste-water treatment field, direct off-gassing of ammonia (a.k.a. Ammonia Stripping) is accomplished by drastically raising the pH of the effluent to force more of the TAN into the ammonia (uncharged) form, which can be off-gassed."
The filter that you are referring to is probably a Bakki shower which will off-gas a small amount of Ammonia before it can be oxidized to Nitrate, but this is only a very small portion of the total Ammonia in the water.The rest is oxidized to Nitrate by typical bacterial action. These devices, however, can remove a large amount of Nitrate if the proper filter media is employed. This filter media must be able, through its porosity,to support anaerobic bacteria (as I stated earlier) in sufficient numbers. These bacteria will reduce the Nitrate level in the water.