Actually, it's more the downhill running and the impact forces of an inefficient downhill form that causes those injuries. Most people who get these injuries due to running downhill do so because they don't build into it, just like you would build your training volume or intensity.
I'd consider it a great idea to run at least some hills every day or at least on most days. I think this is something where you have to find the right balance through experience. In the end, though, Peter really does have the right answer to this. We may all be overthinking this topic. The most important thing, as he states, is to just run.
BTW: Out of curiosity, who are the “they” that are telling you to “keep it flat”?