I suppose. But Sesame Street is like a normal series with seasons and doesn't run a new episode every day. They're over 4,000 episodes. But they're on public TV and not cable, so I suppose that's the next "gotcha"
It just seems like they're creating a hyper specific niche of prequalifiers for what makes their thousand episode run so historic and unprecedented, when there have in fact been a few dozen series in various types of television formats to have gone well over the 1k mark.
That they've entered that tier is historic enough on its own, without trying to claim they're the only ones to do it ever, as long as you don't count these guys, or these ones, or these shows either.