I think we are all aware, acorngen, then the Pinches course of events needs more work ( in the form of obtaining some certs) to back it up - or to squash it.
But looking at the evidence so far, it ticks nearly every box. Therefore, in tbe absence of any other leads (do you have any?) it is worth pursuing to rule it in or out.
From the details originally given by the op, ie an Eileen Winifred Hàydon, born 6 July 1921, parents James and Gertrude dying in 1925 and 1936, Etc, it soon became apparent there was something not straightforward about this - there were no people of those names and the right ages around. Research founnd the Pinches family, and they fitted all the criteria to a tee. Of course, you are right, it is possible there is a completely different scenario - but research has not turned up any evidence to suggest anything else at the moment.
Given the number of things that tie up with the Pinches, it would be a phenomenal number of coincidences if it turned out not to be that, but, if that does prove to the case, then it will be back to the drawing board to consider other possible scenarios - but as to what they could be we can only guess, as there are no other leads.
If there were other leads, then of course they would be being followed up too. But it would be rather silly not to follow this very very strong lead up, just because it might not be right! That is the whole idea - to see if it is! If we just put it on tbe back burner, ignoring tbe compelling evidence found thus far, and hunted around for any different leads, we could be wasting a lot of time and effort if this was the correct series of events all along! Especially, as already said, as yet no other 'ideas'or theories HAVE produced any leads.
There is a lot on this thread for Dickensfan to take in, and think about. Lets leave her to do just that. We are here if she wishes to ask anything, and will willingly help where we can.
(Red writing, Dionysis, meaning you are posting the same time - I'll post anyway, though you have put it a LOT better than I did!)