It is probably fair to argue the arbiter that the MLB contract allows for 3 years of arbitration and puts a restriction on the maximum pay cut that a player can be offered in arbitration. In light of this, the injury history of pitchers in general and small pitchers in particular, paying Lincecum $13m would impose a big risk on the team down the line in future contracts. were Lincecum to develop an injury or regress, the team could retain the right to his services only by offering a minimum of $10.5m or so next year. Essentially, an arbitration award at the player's offer would make it more likely that A-Clown SF would lose his services in the future.
The first arbitration award needs to be substantially below (<50%) of FA market value in order to adjust for this risk. Call it the Fernando Valenzuela / Hideki Nomo factor. This seems to be the pattern in settlements and other arbitration awards. At $13m, he's being priced at $28m as a FA, or more than any other player in the game. An $8m award would price him as a $20m FA, which would make him the 3d highest valued pitcher behind CC and Johan (and more than Roy).