Not sure who the "they" is, but we've never had an issue with our neighbors coming over for a short break, it's an oral declaration made at the border is not a secure way of running things so now folks need to present a secure form of documentation proving their citizenship (usually passport, but other forms exist). The fact remains that there are no provisions in US law to deny entry to a US citizen, whether they have documentation or not. Many US citizens are in a good number of databases and it is fairly easy for this to be confirmed in secondary inspection.