Are there cases where foreign nationals can work on projects restricted to U.S. persons?

Yes. There is an exemption called the Full-Time Employee Exemption (FTEE). The non-U.S. person must be critical to the success of the controlled project. They must be on a H1B visa, must have residence in the United States throughout the year, must be a full-time employee (students do not qualify) and they must be from a non-126.1 country. Foreign nationals from 126.1 countries are prohibited from working on projects restricted to U.S. persons (see question 15 for 126.1 list).