Fascinating stuff.
But the interviewers were so square in those days. I was present at an interview in the later 1960s in Harrogate, UK of Lenny Tristano by a guy from BBC Yorkshire who was a pain.
Brings to mind that famous short film, "The Interview".
P.S. Looks like the Petterstein skit was in 1955, i.e. shortly after the Parker interview. I think there are sufficient echoes to link the two.