Peanut allergies and tree nut allergies

I was just thinking this evening as my husband and I were hanging out by the pool sans children, that even if Amanda were just allergic to peanuts, and not tree nuts, that she still wouldn't be able to eat tree nuts unless they were made in a peanut free plant. Does that make sense? It's because on the can of cashews we were eating it said "made in a plant that processes peanuts". So that means she would not have been able to eat a cashew. I really never thought of this before because it's never been an issue. She will not eat anything that contains peanuts, cashews, walnuts, pecans or almonds even though the last 4 mentioned are really not a nut at all. We just don't know for sure until we get her to take a blood test. That's the only sure fire way to know. So for now my peanut allergic child avoids peanuts and tree nuts. And that's just fine with me.