Well the connection is there in what you just said
Just like how without Burton Batman there would have been no B&R, the same way without B&R there would be no Nolan bats, at least not in the shape and form we got it
B&R went so far off course that they needed someone to come in and reboot with a completely different vision
Sure if Burton Batman never happened I agree someone would have eventually come along and made a batman film, but it wouldn't necessarily have been Nolan, could have been anyone