Could you elaborate why this is not true?
These plants are relatively common, and highly recommended (correctly or not) for people looking to buy their first plants across forums / websites / simple google searches. These plants respond immediately and dramatically positive to high nutrient loads, so when they are struggling people recommend to use fertilizers. Because these plants have typically large roots attached to them, people
assumed they do the heavy lifting in terms of nutrient uptake. They then buy root tabs, place a concentrated nutrient source near the roots, and the plant responds within a few days. In reality, these plants will uptake large amount of nutrients in any way they possibly can, so it's no surprise that they pump out half a dozen large new leaves after a root tab has been used near them. I like to refer to them as "nutrient hogs" not "heavy root feeders" because if the water column is sufficiently fertilized, the plant will produce just as much new growth, debunking the "heavy root feeder" myth - they simple require access to high nutrient loads regardless of they can uptake it.
Other food for thought on this subject:
Large, thick roots are not where nutrients are up-taken - these thick roots provide structure for holding the plants in place, and areas in which fine root hairs can grow from. So when we uproot a sword / crypt, people see huge roots and think "wow these must be where nutrients are up-taken" and that is false - the fine root hairs are where nutrient exchanges happen. Now, uproot an 18" full healthy stem plant, and you will actually see more fine roots, with a lot more substrate attached to them. Soil / substrate attached to roots is a positive sign of root exudates, and there are a lot more exudates on my stem plant root systems vs my crypt / sword root systems whenever I uproot them.
Most substrates allow water (and thus water soluble nutrients) to easily and freely transfer from the water column into the substrate layers, and from the substrate layers into the water column. Because many of the nutrients found in root tabs are completely water soluble, they simple leach into the water column anyway.
Many root tabs made by large companies (Seachem, API etc.) contain over 70% inert material, and less than 1% actual plant macro nutrients that plants require relatively high quantities of. So when these are used, they are not supplying any of the NPK that these plants love most. So if they are growing well, they must be utilizing NPK from some other source (water column, substrate organic matter, substrate cation exchange etc.)