I would personally say giving a demerit here was a bit harsh and un-necessary.  If I was in that situation I would have spoken to them privately and asked them to stop accusing etc.  If he was continuing to harass the other player, they can always use the mute button.  As for being rude towards you, I would have spoken to them privately again to try and calm to the situation down.  If they would have then continued insulting/harassing, then yes, apply a demerit.

We are all different and handle things differently, each situation will be different.

Just my opinion.