In the case of depression, the core stigma is that depression is a weakness, a moral failing. That depressed people are soft, weak, pitiable. This attitude is specific to depression – not even bipolar disorder is seen in the same way, let alone the other diagnoses. They have their own stigmas. Depression’s is weakness.
Now this is why Churchill is a good counterexample. Not just because he’s famous or ‘great’, but because he was famously tough. He faced down Hitler. He was blood, sweat and tears. In the most famous photos of him (and they are famous, out of all his photos, because they correspond to the mental image) he is almost unsmiling – but never despairing. Just resolute.
I think the key here is the notion of Churchill being a counterexample and not just an example of someone with mental health difficulties being successful. It's the notion of opposite action in, ahem, action. By that, I mean that we have someone dealing with the syndrome of depression. Withdrawal, isolation, self-doubt are all part of this syndrome. What we see in someone like Churchill is that he's working to act opposite to those action urges.
Perhaps what makes a good role model is to highlight someone doing behaviors that are specifically opposite to the action urges we're trying to deal with. Again, some research is needed here, but two articles to start the conversation.