That helps, JenCluse. Again, I am very grateful for all the replies, which are helping me pinpoint the answer to this seeming mystery.
I notice, by the way, that the the respondents who are particularly positive that sidedness doesn't matter all live in Australia, which, after all, is upside down and where people drive on the wrong (uh, I mean..left) side of the road. So, I guess they are all used to things being backwards.
Just kidding, of course. Your responses are much appreciated.