At the risk of being a pedantic jerk, the US did send troops to fight on the side of the Czar against the Bolsheviks. They were withdrawn when they found out how bad the Czarists were. http://en.wikipedia.org/wiki/Polar_Bear_Expedition
Sorry, missing reference. I probably overstated the cause and effect, but it does seem to me that it contributed to the morale problems of the American troops.
>> The American commanders in the field reported that the Czarist reign of terror was far more horrific and disturbing that the actions of the Reds. The American forces also discovered that the vast majority of Russians sympathized with the Bolsheviks and supported the revolution. In the end, the American troops were brought home without any fanfare, and the ordeal was considered one of the most ill-conceived interventions in American history up to that time.