We had a local cable company do that back in the late '90s/early 2000s. Zampelli Electronics (it's now Zito Media). They did the same thing. Locals weren't available yet so we had DISH, but Zampelli for the locals. Whenever there was a rainstorm, Zampelli lost some of the cable channels that they had. I knew where that "satellite signal lost" screen was from.
Not quite following you here. Do you mean that you subscribed to Dish for non-OTA content, but also had Zampelli for locals, and that Zampelli carried some of the same channels that were on Dish? And that when there was a rainstorm, and you lost channels on Zampelli, they were the same channels that you lost on Dish at the same time? (I'm assuming that if this was the case, Zampelli cherry-picked channels from their Dish feed to distribute to subscribers in tandem with the locals they carried but that were not on Dish yet. I don't suppose they would have carried the full Dish lineup.)