I think this is another symptom of sites being private. I hope this explanation helps.
When you are editing a post, click Add Media – you will see a link for Network Shared Media. Click that to see media from each of the sites on your network that are currently Public (exposed to search engines).

If, when you click on Network Shared Media you don’t see all the sites listed that you would expect, then the missing sites are not currently Public.
If none of your other networks sites are Public, you’ll see this message:
You don’t have access to any other sites media.
To make a site Public. Go to the the site whose media you wish to share.
Go to Admin Dashboard>Settings>Reading
Scroll down for Search Engine Visibility

De-select “Discourage search engines from indexing this site.” That is, remove the tick in the tick box. That will make the site Public. It’s Media Library will then be shared on the network.
I have the same problem.
I’ve used Robert solution but I need Search Engines don’t index the site for the moment.
I have another problem: media aren’t accessible in Advanced Custom Fields image field.
Any suggestion? I’m going to open another support ticket, but you may know how to fix it.
Regards
Davide
