Spock/Star Trek were on NBC
Carol Burnett was on CBS
I don't think this happened?
There's no reason why a comedy show on one network can't do a sketch based on another network's show. For instance, in 2006, Matthew Fox did a sketch about Lost
(an ABC show) on Saturday Night Live
(an NBC show). Similarly, the famous Shatner SNL episode that featured the "Get a life!" sketch and "The Restaurant Enterprise
" also featured a sketch based on T. J. Hooker
, which was on both ABC and CBS but never NBC. It's parody, after all, so copyright infringement isn't an issue.