But we're asking about the word, "affirm".
Using that site you linked to, the definition is,
af·firm (ə-fûrm')
v., -firmed, -firm·ing, -firms.
v.tr.
1. To declare positively or firmly; maintain to be true.
2. To support or uphold the validity of; confirm.
v.intr. Law.
To declare solemnly and formally but not under oath.
In fact, this is the exact same definition as the other links.
Nowhere in there does it say anything about 'affirm' means to take an oath . . .
In the Jo Nuvark dictionary "affirm" means to bear witness as in agree with what has been attested.