The Soviet Union lost more soilders fighting for other people's liberty than the US?

From the Washington Post:

the claim

"You know, you look back over our history, and it doesn't take you long to realize that our people have shed more blood for other people's liberty than any other combination of nations in the history of the world.''

-- Fred D. Thompson, stump speech in Des Moines, Sept. 7

THE FACTS

A grandiose claim that is hard to justify no matter how you define "other people's liberty." Let's begin by looking at U.S. casualties in foreign wars. (Domestic conflicts such as the Revolutionary War and the Civil War are excluded.)

U.S.
Conflict Casualties

Spanish American War 2,446
World War I 116,516
World War II 405,399
Korean War 36,574
Vietnam War 58,209
Persian Gulf War 382
Wars in Afghanistan,
Iraq (as of yesterday) 4,217

Total 623,288
SOURCES: Congressional Research Service, Defense Department

The number of overall U.S. military casualties, while high, is still relatively low in comparison to those of its World War I and World War II allies. In World War II alone, the Soviet Union suffered at least 8 million casualties, or more than 10 times the number of U.S. casualties for all wars combined. According to Winston Churchill, the Red Army "tore the guts out of the Nazi war machine." It can be argued that Soviet troops were primarily fighting to free their homeland from Nazi occupation. After fighting its way to Berlin, the Soviet Union imposed its own dictatorship over Eastern Europe. Even so, Soviet sacrifices contributed greatly to the liberation of Western Europe from Nazi domination. Soviet forces died for their own country and their own tyrannical government, but they also spilled blood on behalf of their Western allies. . . .

Is this really serious? Suppose that the Americans have encountered more difficulty from the Germans on D-day and the Soviets had been able to go further West. Does the Post believe that people living in that additional area would have been free?