Re: Betty White, I don’t think any specific loyalty to “Password” stopped her from doing “Pyramid” in the 70s — on her first 1982 appearance, she said “I couldn’t quite schedule it” before.
Actually, she appeared on “You Don’t Say!” four times in 1966 and 1967 while “Password” was still airing, and she and Allen then appeared together the week of October 30. G-T were unhappy with that show’s format and (early on) visual similarities to “Password” — Variety’s June 12, 1963 profile of Ralph Andrews and Bill Yagemann said that YDS! “is a program which Goodson and Todman are known to feel is a carbon of their own ‘Password’” — and the desk on YDS! was reconfigured by early 1964. But yeah, regardless of how G-T might have felt about her appearing on YDS!, they couldn’t exactly ban her from “Password” if they wanted to keep Allen happy.