Is PDO_OCI classed as ODBC?
OCI (Oracle Call Interface) is not ODBC. ODBC drivers may use OCI, but not the other way round.

I've never heard of Oracle charging for ODBC drivers/access. In fact, there's no mention of an ODBC component in the global price list (link here).

I would clarify with your vendor - maybe they're trying to extract some cash out of you by supplying/supporting some kind of additional product, or maybe it's just a miscommunication.