You're half right about them having to offer Dunn arbitration in order to receive the 2 high picks.
From 15 days after the end of the World Series until Dec 1, a player who is a Free-Agent may sign with another club and the former club receives compensation.
By Dec 1st, then the former club must offer arbitration to the player.
Doing so makes a lot of business sense to me if they don't believe they can get a better deal than the two picks. They just finished discovering Dunn's value, so they know pretty much what he's worth. I'm certain in the discussions with other clubs, it was brought up, "If that's what he's worth to you now, what will he be worth to you over the winter if we pick up his option and you can have him for a full year?"
Also, there's some misunderstanding on some people's part that the club can't trade Dunn before June 15th. That's not true. That rule only applies to Free Agents that sign "new" contracts during the signing period prior to June 15th, which begins 15 days after the end of the previous World Series. The REDS would be picking up an option of an existing contract if they chose to try to trade him over the winter.
From the CBA:
EligibilityA player with at least 6 years of Major League service time and no contract for the next season is eligible to file for free agency and negotiate with any club.
A player has 15 days from the first day after the World Series ends to file for free agency.
His former club retains exclusive negotiating rights until 15-day filing period expires, and the former club may re-sign the player at any time, during or after the filing period. During the filing period, a player who has filed for free agency may engage in general discussions with other clubs but may not discuss contract details or sign with them.
A club receives compensation if it loses a free agent before December 2. See Free Agent Compensation.
By December 1, each club must decide whether to offer salary arbitration to their former players who have filed for free agency. A club not offering arbitration may continue to negotiate with the player but does not receive compensation if he signs with another club.
By December 7, player must accept or reject the arbitration offer. If the player accepts the offer, he returns to his club’s 40-man roster. The player and club may continue to negotiate before the February arbitration hearing. See Arbitration. If the player rejects the offer, he may continue to negotiate with any of the 30 clubs.
A free agent who signs a major-league contract may not be traded without his written consent before June 15 of the following season.