For a lot of people in the world Europe = USA

But this makes zero sense. Two different continents, values systems, law systems. Not to mention the current USA administration is openly hostile to Europe. So why would anyone confuse the two.

Europe is at the mercy of the USA. Any difference in posture is due to local politics which can swing local elections, but European leaders are willing and eager to do what the US wants.

Sure, I'd agree with that a few years ago. Nowadays when the USA asks for something like just using their military bases for refueling, they're laughed at.

Europe will not be independent as long as there are US military bases there. Saying otherwise would be kidding oneself.

You are aware that the number of American soldiers in these bases is symbolic and their presence is meant to be a deterrent for Russia?