Look up "edit distance"... it is one of the first problems an Algorithms course will discuss that can be solved by dynamic programming. But ya, no way anyone is coming up with that unless they have seen it before.
I 100% would be able to solve this problem without seeing it before. Yes, this is because I've practiced a lot of algorithm problems (and I enjoy them, frankly).
Yes, this is hackable, but relying on resumes like every other industry (which is implicitly relying on hoop-jumping and college prestige and GPA) is a much worse form of hackable. This levels the playing field and is a signal for (1) how smart someone is and (2) how much they prepared for the interview, both of which are weakly related to the job. Further, people who excel at algorithm are very unlikely to be bad at the kind of work at big tech.
It's not perfect, but finding something better at scale is hard.
An algorithm for "do these strings differ by an edit distance of at most 1?" is much simpler, and should be easy to figure out. No dynamic programming required.
This is something I would expect a freshman CS major to be able to solve.
It only requires knowledge of looping, conditionals, and how to work with strings in your language (e.g, indexing, finding length, maybe substrings, etc.).
This is like a less insulting version of fizzbuzz.
People are way overcomplicating this. Any professional programmer could solve this.