I think it’s a coincidence. My (literal) interpretation of “ar chor ar bith” is something like “not at any turn”. “(de) chóir a bheith” is a little harder to put into literal English terms but the closest I can think of is something like “just its being”, i.e. it might as well be. Think of it as being somewhat related to “ba chóir”, i.e. “should”, i.e. would be proper/just. (disregard this italicized part – I stand corrected)
That’s just my way of thinking about them. Maybe a native could offer a better explanation, but they are really just idioms one has to learn.