Lulu , i get where you're coming from, for the simple reason I've been there and it's one of the reasons I keep responding, it's kind of close to my own heart as I recognise your reaction, but I also understand the management reaction as I've been on both sides of that fence. Currently on the management side but I still remember being on the other side.
From a management perspective there is an expectation on you to manage the relationship. Even with the toughest of clients. Not easy but saying to someone reacting badly and under pressure have you got the hump today isn't managing it well. No matter how understandable it was.
If he threatens to do something under your brand you simply re iterate in writing the core principles of the agreement, if they break it and use the brand unauthorised, well my company would do a warning meeting depending on severity and then cut ties or immediately cut ties based in breach of contract.
There is always ways to handle these things. Right now possibly the best bet is to agree a plan of action as a team on how best to handle it, inc what was agreed, what can be provided , when, in what manner and what is not acceptable. Then detail that in writing to them. Have it reviewed first. Then set up another meeting, invite the boss for support, detail an agenda in advance and agree how to address certain scenarios. Try to move it back to something positive where you have a path forward. I'd also apologise to him saying no offence intended and as a way to recognise the complaint and move past it.
It might choke you, but let's be honest, your boss will appreciate you being the bigger person. Oh and stop saying he started it and you could have done worse. Own it and create a plan to move forward.