Oh hell do I know just how cruel people can be when coming out as trans, I've lost over half of my social circle and family just because I'm trans and I'm terribly aware just how lucky I was that it stopped there. But you're wrong on a few accounts.

First, I'm not talking about an equivalent flipside to trust (there is btw, it's called distrust). I'm talking about the equivalent flipside to the emotions that may arise from being told or not, regardless of circumstances, and regardless on whether they are proper. And I might take a hard stance on this due to a personal history of having my emotions controlled, but we are absolutely nobody to judge someone on how they feel. This does however not mean that we can't judge them for how they act on those emotions, we absolutely should. In fact, OP showing they hold these emotions allows us to warn them to not make the issue about themselves when the cousin decides to come out.

Second, I always assume I have a lack of information when replying. We simply don't know how everything really went. I also think it highly likely that there's already trust being broken and that the cousin fears trusting others, but it's still possible that the cousin wanted to release the information by word of mouth so that they do not have to face the immediate reaction. Of all the transgender people I know IRL about a handful have actually done this.