no he didn't, he said he didn't appreciate them enough to thank them. the last war that would actually affect american citizens in north america was world war 2, otherwise do you want him to thank dead people from the 19th and 20th century?
The Germans and Japanese lacked the logistics to directly invade North America. We could have easily turned our backs on what was going on in the world.
However by doing so we'd run out of people to trade with which would have hurt our economy and caused us to go into big financial trouble.
On the flip side the Germans were always looking for super weapons, the heavy water production in Norway was a good indicator that they were trying to reach the nuke. If left unchecked they can just bomb key cities and just invade small portions of the country kind of like how the Europeans conquered the Chinese coast and claimed it as their own.
So yeah in WW2 did have an effect on us, but not quite as people like to play it out in my opinion.
post ww2 and Cold War: It's no that Allies were just as power hungry as the Axis. The Soviet/Commiterm alliance with the Western Allies was a temporary truce.
Stalin wanted more power and more presence on the world stage, meanwhile the Europeans still had their overseas colonies in Africa and Asia and wanted to keep them if possible, and the United States came out as a super power.
Having pushed east to Berlin, Stalin claimed almost every country in Eastern Europe such as Poland(Allies), Czechoslovakia(Allies), Hungary(Axis), Romania(Axis), and Bulgaria(Axis). Pretty much all those countries were turned into communist puppet states or had communists who supported Stalin take over. Yugoslavia and Albania had their own communist uprisings against their Axis oppressors. Stalin did not want to cooperate with the allies, he wanted the rest of Berlin and the rest of Europe.
Western Europe on the other was bankrupted from the war and was in need of rebuilding. Ideally whatever colonies they had left they wanted to keep, but couldn't afford to keep them. Other colonies had felt betrayed/abandoned by their home country and wanted self rule. This was the start of the proxy wars and the cold war.
Shortly after WW2 the soviets received some secrets on nuclear technology from a scientist who worked on the Manhattan project and the Soviets took Czechoslovakia and Poland from the Allies. Warring the Soviets directly was a death wish considering that your allies lacked the man power to fight them directly and also the fact that your old "friend" now has nukes of his own. Meanwhile Greece and Turkey was separated from the rest of the west and was in danger of falling into the soviet sphere of influence. Had that happened, their would have been huge economic as well as geopolitical problems.
So began the proxy wars, rather than fight them directly, we'd indirectly fight them by arming and supporting people who hated the commies/ussr. Communist uprising in Vietnam You say? Give guns to the people that hate them and hope that they are contained. The soviets also had the same problems we had, so they waged proxy wars of their own in the Asian and African colonies trying to gain the influence of more nations.
More influence and puppets = more money and power. Which is what WW2 almost was on a more violent scale. We could have easily turned our back on the USSR and what was going on in the world and that would have just bit us in the ass. Also that line from Fallout carries some truth with it. Wars have always been fought over land, money, resources, power, influence, and ideologies. Never for good and evil reasons.