Exactly. Economics education is terribly lacking, and I really didn’t realize my own ignorance of it until I took a course in it. In the interest of fightin’ ign’rance and all, I give a brief summary below.
According to commonly accepted economic theory, with free trade, there is always an overall social surplus*; that is, the winners win more than the losers lose. It doesn’t matter why foreign prices are low; if they subsidize their industries, then their taxpayers are paying the price (an artifically low exchange rate has a similar impact - they’re basically forcing their prices to be low at the expense of their own citizens), and if they have cheap labor, then it’s their workers who lose. How they get the low price doesn’t matter, the point is that every US consumer benefits from it.
Here’s a nice graph showing the overall benefit from free trade when foreign prices are lower. Let’s say that the good in question is shirts. The line D represents all possible consumers, and how much they value a shirt; for example, I, with my pitiful wardrobe, may value a shirt at $15, while my friend who regularly stocks up on free shirts wouldn’t want another as badly, and might bid only $5. If we line up the population by how much they want a shirt, the result is line D. Likewise, line S1 represents companies producting shirts; some can produce shirts more cheaply and so lie on the left, ones that are less efficient and thus require more money per shirt lie on the right. The intersection between D and S1 is the price that would prevail if no trade occurs.
If there is no trade, we can view “economic benefit” as follows: the triangular region between D and the dotted line P1 represents the benefit consumers get. (Let’s say the price is $10, and I value a shirt at $15; thus, I’d say ‘what a bargain!’ and snatch one up, “gaining” $5 in the transaction.) Similarly, the area between P1 and D represents the benefit producers get: if a company makes a shirt for $5 and can sell it at $10, it’s making $5 per shirt.
Now, let’s look at free trade. The dark line is the “world price” (imported shirts from China, let’s say). If we had free trade, the price would fall to P2. Now, obviously, consumers would win, and producers lose - the question is, by how much? Consumer benefit would be the area between D and P2, and producer benefit would be the area between S1 and P2. If you shade in the benefite before and after free trade, you’ll notice that there’s an extra shaded area after opening up to free trade: the little triangle between D, S1, and S2. That is a graphical representation of the benefits of free trade, demonstrating that it makes society as a whole better off.
Notice that we don’t consider how the lower world price is produced. For our purposes it doesn’t matter! The benefits of free trade appear regardless.
*The one exception is if the domestic price and the world price are the same; in that case, no international trade need take place at all.