The Ancestry article doesn't confirm that it works for all private trees - it merely says that it works whether your own tree is public or private. My tree is private and I've received a few shared ancestor hints, but I think I would have remembered if one had been with another private tree.
PS Please EVERYONE don't post links like that, do it as I do in the newsletter (at the forum you would use the chainlink symbol).
I understood it to mean that we can see that there is a shared ancestor whether the match has a public or private tree, but we won't see the detail for the private tree unless we have been invited? Is it more limited than that?
Sorry - I wasn't aware of the issue with links.