No. Editing an image's title or caption on a project is not controlled by project ownership or team membership. It is controlled by who uploaded the file. If a teammate uploaded the image, only their account can change its title or caption, even though you are on the same team and can edit everything else about the project.
Only the uploader can change it
Every image, video or document uploaded to UNI is its own record, separate from the project it appears on. That record has an uploader, set once at upload time, and the server checks that field before allowing a write: your account has to match the uploader on file, or you have to be UNI staff. Being a project owner, an editor, or any other role on the team does not appear anywhere in that check.
This covers both writable fields on the file: the title and the longer caption text. There is no separate alt text or credit field, so if you want an image credited to a person or source, that has to go in the caption itself.
The change is live immediately, not after Publish
Most edits you make to a project, text, layout, which images appear where, are saved to a draft and only reach the public page when you publish. Title and caption edits do not work that way. They write straight to the image's own record, not to the project's draft or published content, so the new title or caption appears the moment you save it, whether the project itself is mid-edit or already live.
That also means the caption is not a property of the project. It belongs to the file. Publishing a new version of a project does not create a new copy of an image it already used, the new version points at the same file the old one did. So a caption edit is not scoped to one version either: it applies to every version of the project that carries that image, past and present, and to any other project the same file happens to be attached to.
If the uploader is gone
If the person who uploaded an image has since deleted their UNI account, the file no longer has an uploader on record. At that point nobody on the team can edit its title or caption. Only UNI staff can, so if you need a correction on an orphaned image, contact support and ask them to make the change.