>You are explicitly allowing them to reshare your image via the platform -- whether that's an embedded view, iframe, img tag pointing to the original, or copy with attribution seems academic to me. The point is you allow them to send your content on to other people, right?

Via the platform means it's still my tweet, and I have total control over it, and they can't do anything else with it.

Doing other things is not academic in that case.

>They weren't advertising with it[...]putting it in a public collection

Putting it in a public collection for the purpose of..... advertising.

>If I posted a picture of myself on every bulletin board I could find posing with [popular_brand] and labeled it with a big, flashing sign that said '[brand] LOOK HERE', is it unreasonable for that brand to share my image on their website?

Definitely unreasonable. "Look" and "put on your website" are different things.