MySQL/MariaDB Limitations
Both DBAs are right, in a way. There are no limits on the number of schemas, except those imposed by the filesystem, as in MySQL/MariaDB, a schema is basically a directory, producing absolutely no difference for both MyISAM and InnoDB if a table is part of one schema or another in terms of performance or features (you can join 2 tables in different schemas as fast or as slow as if they were in the same schema). I've managed instances with hundreds of thousands of schemas, and the multiple directories were not the performance bottleneck. It is a pure identifier thing. While you can run into some issues, those are indirect to having more or less schemas: for example, in 5.6, a slave can apply changes in parallel only for rows from different schemas.

Why do I say that both are right, in a way? Because having too many objects in the database is a very common source of issues. When you have lots of databases, you usually have 10x or more the number of tables, and that may mean thousands of file descriptors open (that requires memory), thousands of data dictionary cache entries, millions of open table cache entries, etc., which can lead truly to a CPU and above all, memory, bottleneck.