Instagram's terms of use and privacy policy are less explicit about rights to redistribute your content (than Twitter), but there are several lines like "Once you have shared User Content or made it public, that User Content may be re-shared by others." Most of their policies are about absolving them of any responsibility of what happens with that re-sharing.

They initially used her (public, tagged) photo in a photo gallery on the site, and requested permission for standard commercial use (print ads, signage, paid placements, etc). Possibly the reporter's questioning led them to begin to comment-request permission for any photo they pull, but I can appreciate a media team drawing a distinction between the types of usage.

The hashtag is only relevant in that it's reasonable you are drawing interested parties to see your photo, and the nature of a publishing platform means it's practical to expect that photo to be reused. I don't believe anyone could successfully argue a hashtag by itself is explicit permission, but the combination of publication, tagging, and no effort to control usage would seem to be some kind of implicit permission. Practically, as the site policy stresses, once the image is public it's outside of your control. (and without explicit denial, this incident's usage seems implicitly allowed)