If the oath-taker addresses a group upon whom the oath was sworn, but does not know the oath-target is among them, is the oath broken?

Primary text

There are two narrations concerning this. The first narration states the oath is not broken because the speaker did not intend to address the oath-target, which is analogous to a case where the speaker made an explicit exception (Istithna). The second narration states the oath is broken because the speaker intended his greeting toward them, and the oath-target was inherently included, making this situation equivalent to forgetting the oath.