I think this might be better handled in a Tech Support case, but just for a few quick sanity checks:
1. Can that user connect to the AF Database in PI System Explorer and view those tags successfully?
2. Is there any crossing domains between the client where the querying is being made, AF server, and Web API instance?
3. Does querying for other AF attributes on the server or in this database work or does the same error result for all AF attributes in this database when queried via the PI Web API?
A few other things to check out and some questions:
1. What is the client you are using to query the Web API?
2. Can this user authenticate to the DataServers controller? Are there any messages when you hit that endpoint?
3. If so, can you query the tag directly with the streams controller? Can you query the attribute directly with the streams controller?
4. From your other thread I am assuming that you are using Kerberos authentication, can you confirm you have a PIServer SPN on your Data Archive as well as configuring the Web API for delegation to the Data Archive?