The famous Fortune article about the IPO covers all of this:
http://fortune.com/2011/03/13/inside-the-deal-that-made-bill...
They also didn't IPO because they specifically needed the money from the IPO.
The parent comment carefully qualified their statement this way:
"Most successful startups are self funded for most of their life"
Emphasis on most of their life. Amazon was financed by VC for only about the first 2 1/2 years. Uber for example is nearly a decade old and still drinking from the VC tap; Quora is another example of that. Amazon's IPO was just under three years after the founding. Thereafter most of their business expansion was financed by operations in one form or another (including a bunch of debt they took on).