You need good water circulation in an aquarium. That helps distribute the plant nutrients to all of the plants, all of the time. It also keeps the plant leaves cleaner, and it gives the fish some needed exercise swimming against the currents. If most of that circulation comes from an external filter, that is less equipment in the tank to distract you from the fish and plants. For that reason alone, a canister filter is a great idea.
Clean water is insurance against fish diseases, and it tends to reduce algae problems. That, too, by itself is a good reason for a canister filter.
Fish produce ammonia as a waste product. That ammonia can build up in the tank if there are insufficient nitrifying bacteria available to convert it to nitrates, or if there are insufficient fast growing plants in the tank to absorb it. Canister filters can contain media that provide good sites for the bacteria to grow, and water changes, tank cleaning, etc. will not remove that bacteria. There, again, is a good reason to use a canister filter.
I seem to have prettier looking low tech tanks and am able to grow a wider range of species than she................and so do others, and they use the filters..........so I'd say the rational is pretty weak, while some might be fooled by the reasoning, the practical application is quite another matter.
If you wanted to test this theory, you could should leave the filter running and add some NH4 ferts at a low dosing.
Filters or plant surfaces or gravel all have nitrifying bacteria, while some competition occurs, CO2 is the main issue, and if you think about that rather than this NH4 vs NO3 issue, the more CO2 made is really the issue vs the N form.