Your reading of the T&Cs are correct. Theoretically, you're only allowed to check up to 4 bags total for free. If they don't charge you during OLCI though for the 5th-Nth bag you shouldn't have to pay at the airport. I don't recall anyone reporting on this in the past here.
If they try to charge you at OLCI, you could always bring a printout of the website and see if they will waive. Might be worth a shot.
