mysql - Easiest way to copy a table from one database to another?

What is the best method to copy the data from a table in one database to a table in another database when the databases are under different users?

I know that I can use

INSERT INTO database2.table2 SELECT * from database1.table1

But here the problem is that both database1 and database2 are under different MySQL users. So user1 can access database1 only and user2 can access database2 only. Any idea?