Coincidence happens all the time in real life. Sarah Duncan isn't an unusual name, and I expect there are several Sarah Duncans in Bath who are currently fretting in case anyone thinks the video features them.
But coincidences in stories...now, that's another matter. You can get away with a coincidence at the beginning - the initiating incident perhaps - but any further on and the reader will feel cheated. Put your coincidence at the end, particularly if it solves the overall plot, and they'll be furious.
I think it's because coincidence can makes the story all too convenient. We know they happen in real life, but fiction isn't real life, it's pretend real life. The author is choosing what to include or exclude, and most of the characters' 'real life' will be excluded: you don't often see characters doing the boring stuff like getting dressed or cooking every meal. Everything in the story has therefore been especially selected and choosing a handy coincidence to solve the plot feels like the author being lazy.
I believe that one of the reasons we read fiction is to see how other people handle problems. We like matching up our solutions against theirs. We also like to see characters working to achieve solutions. If the problem is solved by coincidence, then the reader is deprived of those two very basic pleasures and whatever the genre, that certainly isn't a happy ending.