Generally the way this is explained is that a base tan provides ~4 SPF of protection, which is far less than the recommended 15-30 SPF of sunscreens. I believe I read once that 4 SPF is only good for maybe 15 minutes of protection.
What I haven't seen explained (and what I want to learn) is how the body's "sun timer" resets. If I'm in the sun for 15 minutes and then go in the shade, how long does it take before I can spend another 15 minutes in the sun? If I'm hiking in a forest, I wouldn't be surprised if 15 minutes of protection is enough to completely avoid sunburn, since you're constantly going back and forth between sun and shade.
Another thing I want to clarify is mutation risk vs sunburn. Does a base tan protect you from mutations at all? I'm not actually sure.