"Did I understand correctly that some people think that the third step should be on beat one and not beat four."
I hope not. Neither beat four nor beat one is "correct". Instead, the step will fall somewhere in between the two. Specifically, it will fall where it needs to in order to support sustained movement of the body with no hesistation.
"If that were the case exactly what timing is being used on the first step of the Reverse Turn."
When I measured it, the timing for the first step of the reverse turn was the SAME as the timing for the first step of the feather. This tells us that timing of the feet is shifted and does not align with the measures - but each figure gets exaclty four beats worth of time.
"Do we then pick up the normal timing."
No. You mantain the offset relationship, as that is what is necessary to create the characteristic body movement of foxtrot.
"It is possible that in a demonstration on one Reverse movement the dancer may arrive a little late. Do they do it on every step."
Yes, they are consistently "late" in the feet (which is to say, on time with the music in the way that matters) on every SQQ figure in the dance.
"Only an idiot would try to copy that one off and try to make it regular."
If that's how you feel, you should quit studying foxtrot, as if you ever succede in learning it, you would have become what you consider to be an idiot.