I might be wrong, but shouldn't this be: "it is I who understands the problem"? While that might sound a bit old fashioned, I think it's actually the correct way to answer the question in English. (Maybe I'm mistaken?)
(A way to check me vs. I: Who understands the problem? I do. Not "me do".)
I'm fairly sure the creators of this course say they teach Welsh as it's spoken so it makes sense for the English translations to be what people actually say as well instead of what some people who write grammar books say is supposed to be said. Especially as I'm not using this course to learn English.
I see your point as well. :) Honestly, I know my point is somewhat nit-picky, and I probably wouldn't have bothered to comment on it, but I have answered with "I" instead of "me" each time and it doesn't mark it as correct. At the very least they ought to accept either one! (I reported it.)