Whether Sinatra had a hand in it directly or not, I dunno, but its definitely true that Palm Springs was a super Conservative, boring place to grow up for a generation of suburban punk kids in the 80s, with all the clubs and bars catering to that middle aged, middle class, golf and cadillacs demographic which Sinatra kind of epitomises.
As often happens, that oppressive environment fostered a really cool, self contained, alternative, DIY scene, and without venues, it was based around generator parties where kids would get high, skate, and listen to music in the desert.
And that birthed stoner rock.