I don't know if this is true or not, but I went to the website where you can buy tickets to watch an Olympic event at Sochi and it seems to indicate that US Citizens can NOT buy a ticket if they wanted to.
I must be wrong. But I cut and pasted this:
The Official ticketing website can be used for ticket sales for citizens of the countries below:
Albania, Algeria, American Samoa, Andorra, Angola, Argentina, Azerbaijan, Bahrain, Bangladesh, Belarus, Bhutan, Bosnia and Herzegovina, Botswana, Brazil, Brunei, Burkina-Faso, Burundi, Cameroon, Central African Republic, Chad, Chinese Taipei, Congo, Cuba, Czech Republic, Egypt, Estonia, Ethiopia, Fiji, Finland, Gambia, Georgia, Greece, Equatorial Guinea, Guinea-Bissau, Iceland, Indonesia, Iraq, Ireland, Italy, Jordan, Kiribati, Kuwait, Kyrgyzstan, Laos, Lebanon, Lesotho, Liberia, Libya, Lithuania, Luxembourg, Madagascar, Malawi, Maldives, Mali, Marshall Islands, Mauritania, Mongolia, Montenegro, Morocco, Mozambique, Myanmar, Namibia, Oman, Palau, Papua New Guinea, Poland, Portugal, Qatar, Russian Federation, Rwanda, Samoa, São Tomé and Príncipe, Saudi Arabia, Senegal, Serbia, Seychelles, Sierra Leone, Slovakia, Slovenia, Solomon Islands, Somalia, South Africa, Sri Lanka, Sudan, Swaziland, Syria, Tajikistan, Tanzania, Togo, Tunisia, Turkey, Turkmenistan, Tuvalu, Uganda, Ukraine, United Arab Emirates, Uzbekistan, Vanuatu, Yemen, Zambia and Zimbabwe.