Actually I believe foreign nationals are provided many of the same rights that citizens enjoy when within US territory. This comes from the language of the 5th and 14th amendments, they refer to "persons" and not "citizens". Also I recall reading that the 5th amendment right against self incrimination doesn't apply at border crossings for anyone.
Border crossings are a legal no-man's-land. You aren't guaranteed any protections under either Constitution, as I understand it. Once you're in the country, you're afforded all the protections (as you said, "persons" not "citizens"), but the border is a different matter entirely.
