Not true. Renouncement does substantially restrict your ability to re-enter the US, however.

http://www.irs.gov/Individuals/International-Taxpayers/Expat...

The rule you are talking about applied only to expatriation between 2004-2008 and then only if you spent more than 30 days per year in the US after relinquishing citizenship.

How the hell does that work? How do they claim to have authority over you once you are no longer a citizen?

Authority is the ability to execute on that authority and the USA has plenty of execution ability.

In practice, it's how extradition works for non-citizens who never set foot inside the USA, or bank account freezes for people who don't live in the USA.

I can't find where I thought read that, so I'm probably wrong.

Only if they decide you did so for tax reasons (which is just a formula they apply to your earnings and assets. hint: if you're going this route, do it fast as these numbers drop every year).