(For example, you just know that some users would be willing to enter their IAM credentials when prompted at some point.)
There's also all the marketing data leakage, and access to the users to promote other companies' products, or maybe even get an affiliate/intermediate cut for AWS sales that were already AWS's leads to begin with.
The email from AWS could easily have said:
We request you put a notice on every page saying "This is a copy of data from <Official Site>. Please check there to verify correctness". If you don't want to add such a notice, then we respectfully request you take this data down, since it is against our terms to host the data in this fashion.