"Clearly one, if not both of them, is lying." What is so enraging John is that this is one of those "I know that you know that I know that you know..." moments. It isn't just that she is lying - that much is patently obvious. It's that the entire regime is lying so smugly and outrageously. They don't care and they don't care that they don't care.
It's the perfect storm of condescension and contempt.
And what's intolerable is that they're going to get away with it.