Tune in, turn on, dial out
What AT&T was really going for with this incongruous approach is anybody's guess. It's doubtful that the staid, conservative Corporate Cogs of the era were going to be charmed by an illustration that looked like it was done on a side of a VW bus by a bunch of hippies. And it's equally doubtful that AT&T thought there was a huge untapped market among the counter-culture for a WATS line ("Tune in, turn on, dial out" perhaps). Most likely, it was just another misguided attempt to create a "hip, cool" ad for an audience that appreciated neither.
The graphics appear to be influenced by Peter Max, the widely known artist/graphic designer who came to prominence in the late '60s/early '70s, with trippy artwork that was thought to be inspiration for this 1968 hit movie's animation:
(I know what you're thinking about this post by now: What a long, strange trip it's been.)