The U.N. stats you quote count only legal immigrants. When you add credible estimates of those in the USA illegally, you're looking at as many as another million per year.
Visa overstays alone can exceed a half-million per year (over 527K in 2015 alone[0] for the most recent numbers available), and that number omits those known to have left later.
The US is not alone in having a lot of illegal immigrants. It's hard to say to what extent the US is exceptional in their number (again, taking into account the size of the US).
However, even if this is an exception, the number of illegal immigrants is still too small to catch up to countries such as australia (under the unrealistic assumption that australia has 0 illegal immigration).
Visa overstays alone can exceed a half-million per year (over 527K in 2015 alone[0] for the most recent numbers available), and that number omits those known to have left later.
[0] https://en.wikipedia.org/wiki/Illegal_immigration_to_the_Uni...