Granting external access only to a public library with the Zotero API key

I'm trying to create an API key which would allow only partial external access to my library. I have copied some entries to a public library group and created a key which has everything unchecked under "private library" and read access checked under the public library I created.

The problem is that when I try to access the public library from Omeka with the key, it reports access is denied. Also the key feed requires user name and password even though I have already logged in. When I enable read access for my private library, Zotero no longer requests for a user name and the feed is accessible with only the api key (as expected).

Is there a way to only expose one public group with an api key?
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