This is the part that gets me the most disbelief and I have stopped trying to defend it, so I will just explain it.

I am a contracting officer.

I have been one for eleven years.

What that means in practice is that my entire professional life consists of sitting in rooms where somebody has just said something that cannot possibly be true, and not reacting to it, because the reaction is worthless and the documentation is not.

You do not say that is a lie in a negotiation.

You say nothing, and you write down the time, and you ask them to put it in writing, and then you have it.