Correct. Any American /Western industry enjoys remarkable competitive advantages (technology, acess to capital, a stable currency, a stable political system, excellent infrastructure, the rule of law) BUT are always going to get hosed on wages compared with any poorer country that somehow makes the same product cheaper or better.
If an industry is uncompetitive then eventually it must adapt or die. Protecting it with tariffs makes an industry into a form of welfare - the taxpayers are subsidising the industries inability to make a profit.
This is the unpalatable part of free trade: I have to change what I do for a living, or how I do it, in order to compete. I can't just wait for a government hand-out.
But the huge advantage of free trade is how much it increases the wealth of both trade-partners. Suddenly both countries have more goods and/or money, and so can afford to hire people for other projects. Many western countries seem to the casual observer to have massive service industries and no great manufacturing base. This is because they are simply trading for cheap food, cheap furniture, cheap cars etc. If people in (say) Britain had to rely on home-produced goods then the country would be immeasurably poorer, even if we had the factories and farms to produce every item ourselves..