Using 'at least' to mean 'according to lowest possible assessment'?

[Vsherry]

To pose my question below, I'm using this definition of "at least:"

Definition: Also, at the least. According to the lowest possible assessment, no less than. For example, At least a dozen more chairs are needed, or The job will take four hours at the least.

Situation:

"Are any of them attorneys?"

"At least he is."

Here it appears "at least" modifies Jim and not "to be," in which case the meaning would change. To me, it seems this would be analogous to "Nearly everyone bought a ball" in that "nearly" modifies "everyone" and not the verb. Is this correct?

I guess what makes this seem odd is that we're not using indefinite pronouns or numbers. If someone said, "At least three are," "at least" would be taken to modify "three, " which technically is a noun without its antecedent. So, it seems "he" should also be fair game to be modified by "at least."

[Vsherry]

I'm sure some of you know the song "God Bless the U.S.A." The lyrics of the chorus read, "I'm proud to be American, where at least I know I'm free."

I take the actual intent of that sentence to be Americans are, according to the lowest possible assessment, free, which means it would need revision. "Where I'm free at least" or "Where I'm at least free," for example. And, if that's the case, I would think "at least" mistakenly modifies "I" where it appears originally. (I wouldn't put it before "know" because I don't think it intends to mean the least of things known, but it's closer to what I think it means than the way I read it now.)

I guess it's also possible that "at least" here means "in any case," but since nothing contradictory to the freedom notion or anything at variance with America's quality was said beforehand, it seems odd. Maybe the line was meant to be a defense against America's critics, but the song never alludes to that. It seems more like a prideful description. So, I think it intends to say what I said above.

To me, the "at any rate" or "in any case" argument might make sense if someone said, "People say America mistreats the poor, but I'm proud to be from America, where at least (at any rate) I know I'm free."

How do you hear it? Am I raising a valid concern, or am I just unnecessarily confusing things? Sometimes I overthink things, but I think this is a valid question.