Thanks very much, Maurice. No, you hadn't answered previously, but I figured I had just worn out my welcome with so many questions. I was therefore happily surprised to see your thoughtful and detailed response. I think I understand all you've said, although my nonscientific brain may take a while to fully digest it all.
So, when you say (I have yet to figure out how to make the block quotes everyone else uses):
"That means that a cross of cultivar A x cultivar B may suggest that cultivar A is pod sterile (because it is known that cultivar B is male fertile from other crosses) but in fact the cross of cultivar A x cultivar C succeeds indicating that cultivar A is not pod sterile. Actually the cross of cultivar B x cultivar A may succeed. That is because in the cross of A x B it is the A female identifiers that are combined with the male B identifiers but in the cross of B x A it is the B female identifiers that are combined with the A male identifiers."
what that means is, in the original cross of cultivar A x cultivar B, when that fails, it does not necessarily mean cultivar A is pod infertile; it could just as well mean that the female identifier of cultivar A and the male identifier of cultivar B are so similar [identical?] that cultivar A's incompatibility system rejected the cross. But cultivar B x cultivar A might work because then it's cultivar B's female identifier checking against cultivar A's male identifier and those are not necessarily a match even though A's female and B's male were, so the cross is allowed?
I have tried setting pods on certain large flowered UFs and had little luck, but when I reversed the cross it worked - but usually this was in situations where the second flower was neither larger flowered nor a UF, and known to be quite pod fertile. But in the scenario you describe, even if it were two large flowered UFs being crossed, doing the cross 'backwards' might work if the apparent pod infertility were actually just an incompatibility issue between identifiers in one direction.
I think I get it. So much to learn! As always, thanks very much for your in depth explanation in a way I can understand.
Rob