Media Library items are protected by the same capabilities as the posts and should be available for view without any limits. The list Media items is restricted if you set the edit restrictions for the role or the user. Is it your case?

It’s not possible currently to restrict role to edit just items created by users with the same role. But it’s a good enhancement to add in a future.
The nearest feature is to list all users ID from that role as the allowed list of authors for this role posts edit restrictions at the “with author user ID” field.

This workaround may not be applicable though if you do not plan to give the ‘edit_others_posts’ capability to this role. A limited read only access to the list of Media library items is not realized.