Thus, a CEO who doesn't treat their cash as the valuable resource it is, is just putting an unnecessary burden on their company.
Peter Thiel isn't advocating paying yourself nothing. His point (and data[1] backs this up), that CEO's making a high salary is a pretty good indicator of Startup that will fail.
If you need a high salary, then being a Founder/CEO probably isn't the right move. You're putting a burden on the company because of your life style choices.
Conversely, if you don't pay yourself anything, you're going to spend too much time dealing with the pain of not making ends meet, instead spending your energy growing your company.
[1] http://blog.startupcompass.co/73-percent-of-startup-founders...