>there may be warnings on the product pages [about regional availability]* IF you are logged in while browsing,*
This is the right way to do it. How're they supposed to know where you're from, where you'll be buying, if you're not logged in. The alternative appears to be to ask every visitor to give their location before you show them anything.
They're not very accurate. They get my country wrong quite regularly.
Also Amazon may know your current location but not where you'll be when you buy something. If I'm travelling does that mean that I can't buy something shipped to my home that would I could buy if I were at home.