I don't get how that is a lie. If it is "ignorance at best" why not go with that?
Since you brought up definition, the one that occurs to me is to "press or urge". Pointing out a discourtesy is, in my kneck of the woods, pressing someone. Proceeding that with calling someone out for not following through and for backing down is textbook pressing. Is this is a regional thing? Where I am "since you insist" is a pretty common term for when you are pressed or shamed into something. As an example:
A: Let's go swimming
B: No, I'd rather not
A: You are being lazy
B: Ha! Well, since you insist... let's go
It is unthinkable in my area (Western Canada) that A would reply "You are lying, I never insisted on anything, I merely pointed out your laziness.". It would be even stranger if that devolved into an attack on B's honesty and integrity. It would be beyond all comprehension if A stated that B would be dismissed until a full appeal was made and reasons why B should every be trusted again were put forth.
A: Have another cookie
B: No, I shouldn't
A: I made them special for you
B: Since you insist, I'll have another.
A: Don't lie, I never insisted, I merely pointed out the fact I made them for you. Don't put this on me. How dare you. I demand an immediate apology. Get the hell out of the kitchen and go to your room until you write me an essay on why I should ever trust you again. You damn little filthy liar.
Anyway, I don't get it. Maybe I never will. I must say, I do wonder if you aren't just having a good deal of fun playing pedantic.
But, I can see we aren't coming to agreement on a common definition. I thought I might help, I didn't.
One thing I missed, where did Eden admit his claims weren't accurate? I'm sorry, I must have skipped that entirely which does me no credit.