After private beta, when would a SaaS startup need a public beta before public launch?

We currently running an early adopter with about 30 users getting ready for a private beta of our SaaS collaboration/project management tool for Agile software development team. Lean Startup camp seems to suggest about charging as soon as possible to validate pricing plan which means there is really no public beta (e.g. already charging since beta). Any thoughts, suggestions, examples?

These software stages of alpha, private, public beta, etc. are more for internal purposes. Out of three software companies I worked in one charged for alpha and two started charging in beta. Better concept is minimal viable product - you charge for that.
I found that customer feedback is a lot different when they are paying for it.

Most often that should be after you fix the most critical bugs or important matters from the customer feedback. You do not want to prolong with the public beta lunch, after all the important issues look ok.