Again you fail to take in the context. Saying 'truthfully and forthrightly affirm' is more than an assertion. Oath is a more appropriate substitution in that usage. Ignoring the context, you can make the case that an affirmation can be a simple assertion. In the context, you can not.
You're just incorrect, I'm afraid.
In fact -- look at the next defintion in Dictionary dot com:
http://dictionary.reference.com/search?q=affirm
af·firm
v. intr. Law
To declare solemnly and formally but not under oath.
"But Not Under Oath".
"Solemnly and formally".
So it just means an affirmative answer that you "mean". Not said lightly, not just for fun, but you mean it solemnly and formally. But *not* an oath!!!
Now, if you wish to keep saying it's an oath, please show me some definition somewhere that agrees with you.