Personally, I think some are missing the POINT here. If I write a note excusing my son from gym for 1 day no matter what the reason is, it damn well better be honored.
On the other hand I have to question if the child handed the note in at all.
In some districts no it would not be honored because it has to be a medical/Dr note. Yes they can and do set parameters around such things (meaning not honoring a parent note and requiring a medical one).