Having watched the tide come in to Morecambe bay many times (only saw a bore once, despite mostly growing up a few miles away), I’d say it’s likely true that you and your galloping horse could drown if you were in the wrong spot when the tide started coming in. That’s because of the channels and unstable mud cutting you off though; it’s actually pretty hard to even pick out where the front of the tide coming in is a lot of the time, it’s a proper labyrinth in parts.
It’s not surprising that a guy whose job is dependant on being the only person who knows the safe ways through the bay somewhat exaggerates the drama though.