Correct. FAA doesn't really care about altitude. Here's the full text of FAR101, so you can read directly from the source.The NAR Model Rocket Safety Code mentions 2,000 feet; however, the FAA guidelines (on NAR's site) only mention verifying altitude ceilings near airports. The FAA guidelines clearly mention the 1500 g (3.3 lbs) and 125 g of propellant maximums. Since the NAR High Power Rocket Safety Code has no 2,000 foot ceiling, I don't see evidence that FAA cares about altitude.
But I could be wrong, hence my question and desire for "authoritative" answers from those more in the know.