I agree with you. If Boras wants more bidders, he should be saying that JD is willing to play wherever a team needs him, including DH. That not only increases his attractiveness in terms of on the field matters, but also in off the field matters. He's a good team player, good clubhouse guy, etc.
The only reason I can think of for Boras to make a statement that JD does not want to DH is to try to get Dombrowski to bid against himself, which would imply that there are no other competitive offers.