Being able to use Amaterasu is a consequence of having the Enton affinity. Enton functions like all other KKG, so it highly depends on one's genes which is determined by the type of chakra awakened from the Mangekyo. If it weren't produced by his chakra, but was only a mere consequence of having the MS like you're saying it is, then every Uchiha would have the Enton affinity.
Nope, Itachi had Amaterasu but he couldn't use Enton. The flames aren't produce by combining nature affinities like Mokuton or Yoton. Sasuke can use Enton because he has a dojutsu that allows him to use Amaterasu which is an element that's not produced via nature affinities.
I made a thread about it last year
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Imo his Enton comes from the fact Sharingan reflects the user's will. He wanted to "
burn down" the past and as a result he awakened an MS ability that allowed him to use Katon at the highest level