No, that's exactly what that particular permission is (from a technical standpoint). What's at issue here is that the tweet the software generated wasn't exactly an authorized use of the account.
What's at issue here is that the tweet the software generated wasn't exactly an authorized use of the account.
Which means that, regardless of the technical point that "access to the Twitter account" gives the app the ability to post, the user did not give the app permission to post.
As a professional certified internet laywer I'd also add impersonation.