The thing about this song is that rhythm, that's what gets me. Now, bear in mind 3 things:
1)Rick Rubin is a pretty 'hands-on' producer; we see him in the 'Funky Monks' film suggesting bassline rhythms to th Flea, for instance.
2)Rick Rubin produced both songs -The Chilis & Tom Petty.
3) The Chili's have produced demos of songs before that have appeared significantly different to the final product (i.e. 'Fortune Faded')
Putting all this together, I don't find it inconceivable that RHCP had that song and that sequence, and Rubin asked them to emphasise it in that manner.
Regarding the lyrics, Rubin has suggested lyrical themes for Keidis before ('The Greeting Song' on Bloodsugarsexmagik).
So, I think it might be a coincedence, but fuelled by some unimagination on the part of Rubin.