Bravo for GLAD!
I'm really glad (ha!) they suggest this. If I were in that situation, I would most definitely feel compelled to mark somewhere on the form or in cover letter that the classification "single" was inaccurate. Checking the 'single' box would have felt like a lie. I think their idea of a cover letter is excellent.
Never linger too long with the ignorant,
throw stones at their talk.
Walk only with the lovers,
the mirror of the soul gets rusty when
dipped in muddy water.