Well your friend is partly correct. Without US manpower and resources it would have been unlikely that the Allies would have been able to invade Italy in 1943 and then France in 1944, opening additional fronts against the Axis powers and relieving pressure on the Soviet Union.

However, the bombing of London (the Blitz) from September 1940 was a strategic mistake by the Germans. Up until then, the Germans had focused on industrial and military targets which had had a far greater impact on the British ability to withstand an invasion. Diverting attention away from those strategic priorities and allowing the Royal Air Force to recuperate helped turn the tide of the 'Battle of Britain' forcing the Germans to shelve their plans to invade by late 1940. So it's unlikely that London would have been 'destroyed' without US assistance. The Battle of Britain also took place over a year before the US formally entered the war and several months before the Germans invaded Russia.

The US entry into the European theatre of operations was of huge importance but that the Soviet Union played an equal, if not greater, part in the defeat of the Axis powers. The failed invasion of the Soviet Union was a hammer blow to the Axis war effort.