MySQL cross-reference between 2 databases with 2 different users

Question

Assume that I have 2 databases named db1 and db2. For some reasons, our hosting service only allows 1 user per database. I have user1 is administrator of db1, and user2 as the administrator of db2. Here is an example query:

SELECT *
FROM db1.table1, db2.table2
WHERE db1.table1.column1 = db2.table2.column2;

The above SQL works if user1 (or user2) is administrator of both db1 and db2. But in my case, it's not. That's why the SQL doesn't work because user1 doesn't have privilege on db2 and vice versa.

How can I cross-reference between these 2 databases?

Thanks.