Actually, US customs has the right to ask for lots of things, but they usually don't. Last summer when we drove to Arizona, the US Customs officer was in a particularly foul mood and my wife didn't give him the "correct" answer to one of his questions so we had to pull over and go inside. After 45 minutes of waiting (there was no one in front of us, he just made us wait until another officer got off their break) we had to produce proof that we weren't going to be a burden on US society ... which meant providing a bank statement, a utility bill showing our address, and a deed to our house. Since we didn't have the last two items (who carries those?!) he told us he could refuse entry to us. At this point, the other officer called him a d*** and told him to stop pestering us and sent us on our way
The next time through, I politely related this story and asked the Customs officer if all of that was required ... his response was, "Yeah, that other guy was being very picky, but those items could be required."
So now, we bring our passports, NEXUS cards, birth certificates, a bank statement, and a utility bill (we leave our house title at home). Since then, we've never been asked for more then passports/NEXUS but what's two more pieces of paper?