Restating this doesn't change the math.
I'll try it a different way: I don't believe there's teams who wanted to pay Cole more and didn't even bid because they didn't think he wanted to go there. I think that may in very rare cases happen---but most of the time, the teams who are willing to pay that much reach out to the agent and try (and that's what I've read when I've seen agents interviewed---they always note there's non-public bidders and discussion). I do think they do not always win, to be clear. In that scenario--player has a preference but is engaging with several teams---I beleive it is a lot more likely teams who are bidding offer MORE if they think a player doesn't want to go there (not less), and so if the publicly reported bids are close or (as in Cole and Judge's cases) lower AAV than where they sign it seems most likely to me they took the money.
Ohtani, in his initial signing, does seem like a guy who made clear he had a specific list and so in his case I do think reasonable to ask if he left money on the table. I have not seen that so clearly this time around, so we'll see.
