I guess there's little point in debating it further because people have different expectations, but just to take the first result in the list I get from the 1851 census:
It is indexed as Thomas Finnimore but the image CLEARLY shows Thomas Livermore with his wife, Mary on the next line. Someone has gone to the trouble of submitting a correction, as I have done countless times, so the result is now correctly listed when you search for Livermore, but it will presumably also be found under Finnimore where other people will be justifiably annoyed that it is wrong

The error is in the transcript, not in the search.
Sorry I can't help with Sophia but for what it's worth she doesn't show on FindMyPast either, at least in a very brief search. But that is where the fun detective work starts

I've had ancestors turn up in the census indexed under a completely different name - copied from the unrelated person on the line above
