No, that's not what we mean, and has never been what we mean. And you seem to be conflating things. We don't talk (much) about "verifiable sources": we base everything on "reliable sources". We talk about verifiable edits, really: we want to constrain editors into only adding material that is verifiable, from reliable sources, accessible to them. Some of the most reliable sources, in the scholarly sense, are some of the least accessible to the general public. (And, frankly, reliability of newspaper reports can vary inversely with circulation. And scholarly monographs with the best information on particular matters are apparently now printed in runs as low as 300.)
So when you say "Verifiable means we can actually verify it to be true", that is not the kind of statement on which so much can be built.
For an edit to be verifiable it has to be verifiable by someone other than the person that made the edit. We're not talking about reliability of sources - it's obvious that a TV show is a perfectly reliable primary source - we're talking about whether someone else can come along and check that what the original editor said is true (assuming the source is right - a wikipedia article can never be more reliable than the sources it uses). It's not necessary that everyone be able to verify it, but a reasonable number of reasonably unconnected people should be able to, otherwise we're open to any number of hoaxes.