A very good point. A lot of people don't know that Frost first made his name doing topical, politically-based TV comedy in the UK. In fact, the members of Monty Python met while working on one of Frost's TV shows. They absolutely despised him, and when they formed Monty Python Frost knew it was going to be big and begged them to let him be a member of the troupe. They told him to ask again sometime around the year 3000.
In the "It's A. Tree" sketch, the smarmy, wood-interviewing host Arthur Tree is essentially a parody of David Frost in all his slimy, celebrity butt-kissing glory.