It's PPP dollars, hence that difference is taken care of.  It is the best measure of real utter poverty there is. And as mentioned, the western world, including the US has none of that. So saying that the US has a poverty problem is quite frankly an utter insult to the real poors of the world.

Another good measure of serious (but not extreme) poverty is HDI, and as noted bot US and Chile is doing very nicely there.

I suspect that you simply will have to just grin and bear it: The myth that liberal politics causes poverty is just that: A myth. Neither the US nor Chile has any huge problem with poverty compared to the rest of the world.

The main cause of poverty is when the mechanism that create wealth break down. That mechanism is trade, and it breaks down mainly because of war or other violent conflicts, corrupt governments and planned economy (in roughly that order of importance).