Just to summarize, since different parts of the correct answer are contained in different posts:

The original question was posed correctly, since you do have the right to refuse. However, if you do so, the airline (acting through the security company, their agents) is required by the FAA to refuse to transport you. They do that by refusing you entry to the sanitized area of the airport. The original question still has to be asked because the right to inspect your bag is not unqualified. After over 20 years of routine airport security checks, people are supposed to understand this by now, and it's a little surprising that even some FF'ers apparently don't. This could all be explained in greater detail along with each request, but most people, IMO, would find this adding an unnecessary delay to the process.