I don't know about you, but the club control, arbitration, free agency rules have always confused me. I found this. It seems to clear up some of the issues:
"For a player to be eligible for free agency, he must have a minimum of six years service time. This is different from the arbitration rules, where the top one-sixth (in terms of service time) of the players between two and three years of service are eligible for arbitration."
http://www.baseballamerica.com/help/faq.html#fa
This sounds like arbitration eligibility starts after either 2 or 3 years of service and free agency after 6. If that is the case, the team can retain a player for 6 years if they a.) submit to arbitration or, b.) sign the player to a contract to avoid arbitration.
I've noticed the A's tend to sign promising players to multi-year contracts rather than go to arbitration, thus avoiding the possibility of having to pay market price :-)