I agree with your "searching under the lamppost" theory. If I'm Japanese and I see an obscure kanji, its phonetic (component) only gives me information about its onyomi, which is almost certainly some wildly obscure loanword from late medieval Chinese that isn't even in my recognition vocabulary, much less my productive vocabulary.
It might also be true that I don't know offhand the onyomi of other characters with the same phonetic—in real life I'm a native English speaker, a second-language speaker of two or three Romance languages, and the kind of person who likes to go around thinking about obscure etymological trivia, but I was today days old when it first occurred to me that "suspicious" was probably etymologically "overseeish", cognate with "perspicuous", "spectrum", "speculum", etc. (I was right about "spicious" but wrong about "sus": it's actually "uplookish".)
So it would be totally unsurprising for even a highly literate native Japanese speaker to know the onyomi of numerous characters sharing the same phonetic, but not have that shared sound come to mind when looking at a novel character with the same phonetic, even if they can guess which part is the phonetic and that the obscure word is in fact Chinese in origin. And the YouTube video is likely edited to focus on the people who got things most entertainingly wrong.