That is a great point. However, that solves the short term problem, but not the long term problem. Unless you can say that there will poor countries that are willing to allow limitless emigration to the US forever and the immigration solves the social/welfare problems instead of exacerbating them. Immigrants are usually poor, how are poor people going to solve welfare problems? Immigration has solved Europes population problems, but certainly not their economic/welfare ones.
How these transitions effect social/welfare problems is really another topic (although an equally interesting one - and I feel as though I would need to do more research to give my informed opinion). And you are right that immigration solves no ones long-term problem if the whole world develops and has a below replacement level fertility. However by 2050 I feel as though life expectancy will be much longer and humans will not be the only sentient beings on the planet (robots will be as well). So the situation is a little hard to predict.
I just thought I'd put this out there since the original article didn't seem to give the other side of below replacement fertility levels.