A childhood belief about tv shows

There is a very famous British children's TV show called Blue Peter which is almost as much of a British Institution as Big Ben. When I was a kid the presenters, John Noakes, Peter Purves and Valerie Singleton in those days, used to say at the end of each programme "we'll see you on Monday/Thursday". I thought this meant they could see me sitting on my parents' settee like I could see them on TV. When I studied 1984 for English in high school the phrase "the telescreen not only transmitted but received" reminded me of what I had thought about the Blue Peter presenters when I was a kid.