Here is everything Chaturbate provides affiliates in their api and nowhere does it state that images can't be stored on affiliate's servers:
- username: max length 111 characters
- room_subject: max length 200 characters
- is_hd
- is_new
- tags: max length 50 characters / tag
- seconds_online
- gender: Can be "f", "m", "t", or "c" for "female", "male", "trans", and "couple".
- recorded: "true" or "false".
- current_show: "public", "private", "group", or "away".
- chat_room_url: A url with your affiliate code in it.
- image_url
- image_url_360x270
- block_from_states: This field is no longer populated.
- block_from_countries: This field is no longer populated.
- iframe_embed: HTML for an iframe embed with your affiliate code in it.
- num_users: Number of users currently viewing the room.
- num_followers: Number of users following the room.
I emailed Shirley and Suport to clarify.