All tourists can be rude and annoying.
Japanese can be pushy, Brits can be obnoxious, Germans can be aloof and arrogant, and so on. There are reasons for the stereotypes.
But the Japanese can be quite polite, the Brits can be charming, and the Germans can be insightful.
Are Americans any worse than the rest? At times. When we demand others conform to our culture (or lack thereof, as the French might say) in their countries, we display our ethnocentric worst. Perhaps if we manage to survive a few hundred years more, we'll grow out of it.
You are being handicapped by logic. People like Ms. Lake are LIARS. Reality and facts have no bearing on their thought processes. For them, the myth they believe is more powerful than any reasonable argument.