The sure sign you need an independent board.
I've worked with enough organizations to know that every organization is different. And yet oftentimes every group is unique in exactly the same way, if you catch my meaning. "You couldn't possibly understand our issues with X." Hmmm, try me.
In any case, there are no hard and fast rules but certainly some of the guidelines are pretty reliable. One rule of thumb with a nearly flawless track record is that organizations which claim to have no need for an outside, independent board of directors are invariably the same organizations which could most benefit from one.
If you have a tight group of uber-aligned thinkers who move unconsciously together, then a board might just provide the friction required to improve your potion and reign in some of your wilder ideas. And if you have a disconnected, scattered collection of warrior chieftains defending their own fiefdoms, then a board might help bring some cohesion and accountability around a few core values.
If you hear yourself arguing against adding outside directors to the board because of the influence, rigor, and accountability they could add, it could be time to ask: What are we afraid of, and why?