Is it true though?
I mean, for the most part. You would have 13 months of 28 days with 1 leftover. Make that one new year or something. Leap years would just have another straggler day, lump that in with new year I guess.
The moon thing is wrong though. The moon does not operate on a 28 day cycle.
As for Monday being the 1st and Sunday the 28th, that wouldn’t matter at all. Any day could be the start of the month.
364/28 = 13
The Human Calculator Calendar by Scott Flansburg: https://calendars.fandom.com/wiki/Human_Calculator_Calendar
As thewitchslayer says, the lunar month has 29.5 days. English common law has a “lunar month” which is 28 days though.