[Chibi-Chan]

Lacking "basic knowledge" about writing music has nothing to do with being able reading sheet music. Just because you can read sheet music doesn't mean you're able to compose on your own. Even composing on your own and "basic knowledge" about writing music are two different things. You can compose your own melodies without knowing anything about proper compositions - that's basically the case for Ayu. The melodies Ayu composed back then are clearly written by someone who has zero knowledge about how to write music in the first place. Someone who would have learned it would never compose the melodies Ayu did. I guess that's what I, and many others, love about her compositions, that they are so imperfect from a musical point of view but yet not that simple.
Giving Ayu zero credit for knowing how to read sheet music is a bit ignorant and Ayu would make a fool of herself if she didn't learned it in the past 16 years. And like I said, it's an important skill when recording vocals.

Edit: even if Ayu was the "by ear" type, the fact that she had problems with her hearing since dome tour and therefore since 2001 would make it unavoidable for her to know how to read sheet music. Because of her hearing problems and the loss of her hearing a few years later she would have never been able to rely on her hearing alone when recording.
And that "TONS" of musicians couldn't read sheet music is an exaggeration and the ones who claimed not being able to read sheet music were able to read chords for guitars and played the guitar very well. Even those legendary ones had to rely on some "tools" regarding music. The idea people are able to compose without knowing nothing at all about music is a myth.