They have to let US citizens in, but they can detain you for a reasonable amount of time while they investigate you, which could be days. They also don’t have to let your stuff in. If you don’t answer their questions, you are very likely to get into the country late and without your possessions, so only do this as a last resort.

(This is in contrast to interacting with police within the country, where they can’t search your stuff against your will or hold you without probable cause, and not answering questions is a good default.)