Maybe there is some confusion here. The counter mentioned at the start of the thread was counting people, not rates. A ranking of countries by birth rate does not provide information on contribution to population increase as one also needs the population of the country. The US is a big country, so even modest birth rates can produce large increases in poplation. See below.
http://www.prb.org/Content/NavigationMenu/PRB/Educators/Human_Population/Migration2/Migration1.htm
The volume of legal migration has fluctuated since the 1930s. Immigration has accounted for an increasing portion of population growth as American women began having fewer children. Today one-third of the U.S. population growth is from net migration. The U.S. Census Bureau projects that the U.S. population will reach 403,687,000 by 2050. Of this projected growth, 36 percent may result from immigration, with 46,691,756 new immigrants being added in the next 50 years.
http://www.findarticles.com/p/articles/mi_qa3761/is_200212/ai_n9157094
The U.S. population is growing as fast as or faster than any other more developed country. Between 1990 and 2000, nearly 33 million people were added to the U.S. population-a group nearly as large as Argentina's population, and the greatest 10-year increase ever for the country. This growth is in stark contrast to the slow or negative population growth in other more developed countries, and reinforces the United States' demographic position in the developed world.
At 288 million in 2002, the United States is also the world's third-largest country. Although it is well behind numbers one and two-demographic billionaires China and India-the United States remains the largest more developed country. Russia, with 145 million in 2002, comes closest in size, but its numbers are dwindling because it has more deaths than births each year. Japan-at 127 million the third-largest more developed country-also faces population decline in the near future. Other more developed countries, a group that includes the rest of Europe, Canada, Australia, and New Zealand, are far smaller and are not expected to grow much larger over the next half-century. The United States, in contrast, is projected to add nearly 140 million people by 2050, bringing the population total to 420 million.
While the U.S. population increased substantially throughout the 20th century, the percent increase each decade varied from 21 percent between 1900 and 1910 to 7 percent between 1930 and 1940. After holding steady at close to 10 percent per decade between 1970 and 1990, the pace quickened in the 1990s. The magnitude of growth during the 1990s surprised even the Census Bureau and population experts who track demographic trends. The 2000 Census count came in about 7 million higher than expected. Many demographers think that much of this discrepancy is explained by international migration: More immigrants settled in the United States and fewer residents moved abroad than the Census Bureau had anticipated.1
Fertility has been the driving force of population growth in the United States. In every decade of the 20th century, births far outnumbered deaths, generating natural increase. In 2001, 4.0 million babies were born in the United States, while 2.4 million people died. The annual number of births determines population growth, but this number, often measured as births per 1,000 population, reflects the share of women of childbearing age as well as the average number of children each woman bears. Demographers often look at the changes in the average number of children per woman to detect trends that can be used to forecast future growth. The total fertility rate (TFR) is often used to measure the average total number of children a woman would have given current birth rates.