The U.S. had the "luxury" of stockpiling while they were isolationists. Yes you guys deserve full credit for the victory over the Japanese in the Pacific, but lets not pretend that you would have won a straight up war against Germany (unless you dropped the bomb, which is some of the technology that Churchill admired) had the British and their Allies and the Russians, not been tough, resilient bastards for years in advance. Remember, there were 5 beaches at Normandy. 2 won by Americans, 2 by the Brits, and one won by the Canadians. Those Canadians were the first to reach their objective and rendezvous with the American / Canadian joint force of paratroopers that had jumped into Europe... While there is no doubt that we needed the Americans to overcome the Germans, y'all didn't come close to winning that front on your own.
There are extremely competent soldiers from other nations as well. Part of that is because some nation's have highly professional militaries. They may be smaller in size than that of the U.S. but some of them are much more extensively trained than the average U.S. soldier because they are career soldiers, which isn't always the case with a large segment of Americans forces.
I don't think there is a person on the planet that doesn't respect the capability of the United States Military, or the men and women who man it, but there are fabulous soldiers, aviators and Marines from other countries as well... I've mentioned this before, but I'll mention it again.
In Afghanistan, the officer in charge of all participating special forces was American. He had the choice of using SEALS, DELTA's, British and Aussie SAS commandos, but he went on record saying that his first choice for all direct action and counterterrorist missions were Canadian JTF2, our tier 1 equivalent, who happen to have extensive training in the missions that were so widely necessary in Afghanistan. That's not to say they are "better" than anyone, but a smart leader knows who is most capable and suited for a particular situation. While highly unfortunately, their were SEALs killed in the line of their duty in Afghanistan (God Speed to them all), those same JTF2 operatives managed to escape without a single casualty, while being involved in some of the most dangerous and complex operations.
This is why we all train together. We bring different specialties to the table and we make each other better as allies. In my MO (combat medicine) our Medics are much more extensively trained than your Whiskeys and Marine Corpsmen because our military tends to only hire certified paramedics with a 2 year degree in paramedicine, then we get another year of combat medicine training. 3 years, as opposed to several months of training.... That said, American medics often have much more action on their belt, meaning they have extensive knowledge of executing our trade in the field. That knowledge is priceless. Therefore, when we get together to train it usually ends up with this. Your medics teach our guys and gals the tricks of the trade they picked up on the fly while in a combat situation. They stress the principals of keeping people alive. On the other hand, our Canadian Med-techs offer extensive knowledge in advanced procedures and clinical and system knowledge that can be integrated into the experience our American counterparts have.
Churchill's comments were not meant as an insult to American soldiers or officers, rather as a compliment some of your allies.