Agreed.
Do most equate the level of Championship with MLS?? I've heard that many think MLS is below championship, but I honestly don't know.
I think it is the noise. If you want to argue it is slightly better, that is fine, if you want to argue it is slightly worse, that is fine too. The gap is small enough that it is kind of inconsequential.
The key to these discussions is whether one is concerned with quality of league top to bottom which relates to the quality of competition the player plays against week in and week out, or whether one is concerned with the quality of the individual team which relates more to how much competition a player will have to even get on the field.