"It's Only a Constitution..."

[Farnham]

From what I've been told,if you leave US territory and then start using a passport for which you can legitimately claim citizenship, the US generally looks the other way.

Thats about right. It's often claimed dual citizenship is illegal in the US, and perhaps it is, but its rarely enforced.
One Canadian/American dual citizen put it like this: If you call the State Dept. saying you want a dual citizenship, you'll probably be told it's illegal. But if you call the State Dept. saying you are a dual citizen, you'll probably be told it's OK.