I have been on the regimen for almost two years now and I can say if you are careful it doesn't consciously do that. The use of BP and AHA does make your skin more sun sensitive that is why it is always advised to use some SPF.

What nicmic said, the sensitivity to sun is the most likely cause, so SPF is important, regimen or not.

It's not just direct sunlight, sitting in the shade on a sunny day, or simply walking about on a cloudy day can still get you sunburnt.