Also not an employee or shareholder, but a Coinbase user. I don't know that Brian's set of tweets does anything to my confidence in Coinbase as a company. These tweets are trivial.
The biggest threat to my confidence about Coinbase is the structural parts of it, the fact that they are a growing centralized for-profit company responsible for a large amount of assets.
On this trivial (to me, maybe not to Coinbase) Twitter matter: I can see how both sides would go public like this. If you are an internal employee and you think there are C-level personnel changes that should be made, the odds are definitely not in your favor to propose such a thing internally. The risk is high that there will be retribution (whether direct or indirect). Going public is a way to drive attention to the issues, and incentivize that execs act in a legal manner in their responses.
I can also see why Brian would want to address this. Employees are airing their dirty laundry publicly. Shareholders and users can see this. If all you saw was this petition, it would certainly raise a lot of questions. It needs to be addressed in the arena in which it was surfaced by leadership. Where I think Brian is going wrong is he is being 100% defensive and 0% open-minded/empathetic. What about Coinbase's environment led to employees feeling the need to go public like this? This should be a time for some introspection, to hopefully ensure this doesn't happen again.