No, they wouldn't be taxing US airlines in the US, that's ridiculous FUD and just typical of the rubbish spouted about the ETS.
If the flight doesn't originate, stop or terminate in the EU, and if it's not a EU airline, then the flight won't be taxed. If the flight originates, stops or terminates in the EU, or if the airline is EU based, then it will be taxed.
So yes, it is taxing something thats happening in the EU. Foreign airlines not flying into or out of the EU won't be affected - just like how airlines that don't fly into and out of the US aren't subject to DOT fines.
If an airline doesn't like it, stay out of EU destinations.