If you refuse to answer, they just don't let you in. Someone who doesn't already have some kind of legal status in the US has no right to enter, so they can turn you away for any reason at all.
Actually, they naturally do, but there is a specific law to prevent entering unless some specific criterions are met.
Outside of dictatures, people are born with all the rights, and the law is made to remove them. Those law are generally made to protect the rights of other. The main law that doesn't enter this category is immigration law since changing country doesn't remove any freedom to the citizens of the country of arrival.
