Hi FHAY,
According to the tags in your post, I notice that you are using Office 365 Enterprise plan tenant. Could you tell me whether the user is able to change the profile picture if you give the other admin role (Password administrator, Service administrator)?
Even though the global administrator which synced from local AD can change the profile picture, we recommend customers change attributes for users from the local AD, because this will bring better and smooth user experience and avoid potential issues or risks.
Thanks,
Bourne Zhang