I think the underlying assumption is that the company will grow very quickly, so that when it comes time to pay you back they are paying you back with a small fraction of their revenue. Look at Netflix, for example: ten years ago they had 1.67 billion in annual revenue. Last year they had 1.87 billion in net income, and they are still growing. There are certainly some ridiculous valuations, but that quote is ignoring both the fact that businesses grow and that not everybody needs a 10 year payback.

More generally, the reason there are high valuations for companies that are growing users by selling a $20 bill for $18 is that they can drive out all of their competitors who can't afford to burn money. Once those competitors are gone, the survivor can raise prices, lobby governments for regulations that make breaking into the market very difficult, and generally employ anti-competitive practices to take advantage of their situation. If they're able to do this without being smacked down by anti-trust regulators they will be a money printing machine. These high valuations mean that the market thinks that governments will remain toothless and easily controlled. It's a depressing future to think about, but there's a pretty high probability that this is how it will be.