It is not true that: "The United States enjoys net immigration with respect to almost all other countries in the world, and has throughout my lifetime."
First, those are two different metrics. I read him as saying that the United States has net-positive bilateral migration with almost all countries in the world; i.e. for any given country X, more people are emigrating X->USA than USA->X. That doesn't imply that the U.S. would necessarily be the #1 country in the world for overall immigrants-per-capita, only that it wins most pairwise comparisons of "voting with your feet".
Secondly, even by your metric, the U.S. is pretty high up. Of the 30 above it on that list, many are microstates, which makes per-capita statistics fairly wonky (some individual American cities would be that high, too, if they counted separately as microstates). And, many aren't even countries at all (e.g. French Guiana, or the Northern Mariana Islands... a 50,000-person U.S. territory). If we ignore those, then things look quite a bit different; the U.S. ends up #15 among independent non-microstates. And a lot of those are places you don't really want to move to if you have a choice, e.g. Burundi ranks highly because of regional wars and refugee camps. Among the US's peer group of non-micro developed nations, it's #6, behind Singapore, Australia, Canada, Ireland, and Portugal.
Top 5 out of 8 wouldn't be doing so well... but the point here is not about absolute numbers of people migrating, its about the types. Does the US want entrepreneurs or just those with family members?
The US is ranked just 31 in the world for net migration rate: http://www.nationmaster.com/graph/imm_net_mig_rat-immigratio....