Well, I can think of a couple of possibles but I suspect that there's something more ... tangible !!!
First, its an acid song and most of the acid around the San Francisco area at that time was manufactured by Owsley Stanley, affectionately known as Bear and "manager" of the Dead. I believe that the proceeds from this enterprise may have funded the Dead in the early years.
Second, the Dead were the house band for the Happenings organised by Ken Kesey's Merry Pranksters (of Psychedelic bus "Further" fame) and at which large barrels of fizzy pop (kool aid) laced with acid was available to anyone. LSD was legal in America at the time. These events were documented in the book The Electric Kool Aid Acid Tests.
Maybe third .. the Airplane lived just down the street from the Dead in Haight-Ashbury.
And perhaps fourth .. Garcia often played with them, particularly in the later Jefferson Starship days.
... which is as good an excuse as I can think of to listen again to this ....
https://www.youtube.com/watch?v=_Disl35BIzM
The noodling guitar in the breaks and choruses is unmistakably Jerry.
That closing phrase "It ain't what you want, it's what you need" still brings a moistness to my eye.
And the whole thing still makes my spine shiver.