Common sense?

Scientific American: Fact or Fiction?: Living People Outnumber the Dead
Booming population growth among the living, according to one rumor, outpaces the dead.

I read in the above article about the question whether the living people outnumber the dead. From the article:
"The human population has swelled so much that people alive today outnumber all those who have ever lived, says a factoid whose roots stretch back to the 1970s. Some versions of this widely circulating rumor claim that 75 percent of all people ever born are currently alive."

Unless you believe the world started populating around the time Jesus supposedly died on the cross, this can't be true.
A highly simplified model could be the following:
If we start with 1 couple (2 people), which produce slightly more than 2 children who (when their time comes) produces more than 2 children ... and so on, we can ask the following:

When is the sum of all the people produced equal to 6 billion (current population)?
If we take as an exponent 1.025 (so that 1000 couples produce 1025 new couples), it takes less than 800 generations. Of course, we didn't take anything in account (plagues, food shortage, wars, infertile men/women, gay couples, abortions, women who are never in the mood, ugly/stupid people who couldn't get a date, etc), but the exponent is very low.
Even if we take as an exponent 1.002 (1000 couples produce 1002 new couples), we need less than 8200 generations to accomplish the total amount of 6 billion people who are dead. The first homo sapiens originated from about 200.000 years ago from Africa (Wiki).

Estimations for the year 2050 range between 7.3 and 10.7 billion people, giving a much larger exponent than we took.
I think we can safely say it's bullshit to say that more people are alive now than that ever lived.
(The article comes to the same conclusion; it just surprises me that people could ever believe such a statement)