He says it saves money and time (time being that you don't have to set up another piece of gear) and you don't have to sync it up in post. He notes that at professional shoots they don't record to camera. But feels at our level it is unnecessary.
This is very different than your feeling that you will get
"better" audio recording to a dedicated audio recorder.
Now your friend is correct. You can save time in both
production and post by recording directly to the camera.
If you are paying people (or even just feeding them) you
have a boom op and not both a recordist and boom op.
These are compromises that need to be considered. This
isn't the what is best, question you first asked.
For many years I used a mic attached to the camera. I
still do on many shoots. You can get fine audio but you
lose audio control.
Just to place it in context; it's only in the last 15/20 years
that syncing audio in post has been thought of as an extra,
time consuming step. And that ONLY when shooting video.
Syncing audio to picture has always beed a normal, standard,
expected part of post production.