Earlier this year, Mashable won a motion to dismiss a copyright infringement case (see link). Mashable was accused of infringing the copyright to a photo because it embedded a photo using the Instagram API. The court found that Mashable had a valid sublicense from Instagram to display the photo using the Instagram API. Based on this case, it would appear that Instagram users that set their profiles to public are granting users of Instagram's API a sublicense to embed their images.
McGucken v. Newsweek LLC, Case 1:19-cv-9617 (SDNY) is another copyright infringement case where the alleged infringer embedded a photo using the Instagram API. Newsweek argued in its motion to dismiss the Mashable defense -- that it had a sublicense from Instagram to use the copyright holder's image (see link). But, the court denied the Mashable defense because there was no evidence of a sublicense.
Asked about the McGucken case, Instagram allegedly stated "While our terms allow us to grant a sub-license, we do not grant one for our embeds API.... Our platform policies require third parties to have the necessary rights from applicable rights holders. This includes ensuring they have a license to share this content, if a license is required by law." (see Ars Technica link). Some commentators say Instagram's proclamation makes the Mashable defense untenable. I disagree. Instagram can say whatever it wants about how it believes the agreements should be interpreted (which is extrinsic evidence). What matters is how the courts will interpret the language of the agreements.