The Blazers are in luxury tax territory, so it's not like letting Oden go frees up room to sign another player. Your choice is Oden for $10 million/year or a string of minimum salary guys for less. In theory, a quarter season of Oden might be more useful than some journeyman scrub (but not worth that much money, of course).
If Portland lets Oden go, they are pretty much committing themselves to being the sort of team that makes the playoffs and exits in the first round for the life of Brandon Roy's contract.
And that Eastern Conference executive does not sound like Danny Ainge at all. One of the great things about Ainge is that he is not risk-averse. The anonymous executive is afraid of looking bad and is basically saying that you should resign with Oden because it is better for him to be a failure in Portland than a success anywhere else, or at least that's how I interpret his words. If Ainge thought that way, he would have re-signed James Posey and kept Perkins because he would have been afraid of looking foolish for not standing pat.