I'm glad to see someone else bring this up. It can be confusing to a lot of people who don't know the "lingo" of color genetics. But you are completely right. I think a better use of the term would be "homozygous black FACTOR" meaning the horse cannot sire a chestnut foal. I always advise everyone to test for Agouti when testing for black and I believe UC Davis does do them both at the same time as a rule.
If a horse is EE and Aa they "can" sire black as long as the mare is not AA but as you point out, if one parent is AA, even though they are also EE / homozygous black factor, they will never sire black. Everyone should test both potential parents for Agouti before attempting to breed for black.