I've heard this etymology before, but the article would be a lot more convincing if it showed an actual in-the-wild example of the "intermediate form" of the symbol, with the P and S exactly superimposed on each other...
http://monoskop.org/images/2/21/Cajori_Florian_A_History_of_...
Edit: thanks Nemo!
I see no reason why make something up that would be quite easy to disprove by looking at old records.