Yes, but what if someone also rejected that statement as being an oath prohibited by the bible. In other words, what happens should someone refuse to swear to .... ANYTHING?
My wife asked me what happens when one says I do not recall. If it can be shown that your failure to recall is a ruse i.e. they can show you did recall the subject recent to the questioning, like if they recorded a conversation with you mentioning the incident about which you claim no knowledge, you can go down for lying.
IMO, the best choice is to say nothing if questioned by an agent: do not cooperate, do not furnish records, do not lie. If served process, just furnish what is requested, do not destroy anything unless you are HC. If called to testify, do not lie. If you plan on lying, take the fifth. If they give you immunity, you could go to jail for contempt if you don't answer which is a personal choice but do not lie.