I can see how that statement could be mis-interpreted. Most of us have fish in our tanks and feed heavily, and the nems eat what they catch. So typically people don't need to supplement what the nem receives by directly feeding them.
Furthermore, many beginners tend to want to feed their nems a lot, and as a result they overfeed which does more damage than good. The pieces might be too big, the wrong type of food, spoiled food, etc. the list goes on and on. I recently read a post there the person fed his nem cooked shrimp.
I should also point out that many nem owners also have clowns that often take food back to the nem (newbies see this is the clowns feeding the nem, which we know is not the clown's intent).
So, in short, saying that we don't need to directly feed our nems is an accurate statement. It's different if someone has a nem only system, but these people tend to be more advanced aquarists who know when their anemones need to be fed.