(Come to think of it, a person who is convinced that the mind is in the brain, and thoughts are located in the brain, would find it objectionable too.)
Of course, the dictionary exists to get us to use our words straight. I'm discussing a point that's germane to a philosophy class, so it shouldn't be construed as a criticism of the dictionary.
Be that as it may, it is essentially the same definition that Ayn Rand used.
As for thoughts in general being "objective," that's actually somewhat irrelevant to the point at hand. Rand stated that "Reality exists as an objective absolute—facts are facts, independent of man’s feelings, wishes, hopes or fears."
She furthermore claimed that the moral principles she espoused, were in some way objective, according to that definition: discernable through the exercise of logic and reason, applied to the evidence of objective reality provided by our senses. Among other things, for these things to be objective, this implies a requirement for her principles to be measurable.
And thus when Rand claims that "the pursuit of his own rational self-interest and of his own happiness is the highest moral purpose of his life," she either means it according to the dictionary definition, or she is willing to accept a subjective state as the "highest moral purpose" of her philosophy.
We must take her at her word that she envisions "happiness" as a fully objective property. And thus the requirement that "happiness" must be observable, measurable, and in some sense part of objective reality, independent of hopes, fears, and so on.
The problem comes, not from the definition of objective, but rather the insistence that "happiness" is somehow objective: it is a fact,"independent of man’s feelings, wishes, hopes or fears."
Just to place happiness that context is to highlight the irrationality of Rand's claim.