Is it true that the moon radical 月, which is used in words of time and bodily organs, was originally two radicals – 月 and 肉?

I know that the moon radical is used a lot in kanji regarding time and months. I started to ask myself why so many kanji related to organs and the body, like 肝, 肺 and 崩, have the moon radical. Then I noticed that 肉, if you try the lines diagonally within the enclosure, it kind of looks like ribs of the chest, and if the lines are all parallel, it looks like the moon radical. I thought it was cool. I can’t find much about the history online.