Warning: Very coarse and quick explanation incoming. The details can be worked out if you're interested.
Not a biologist here but a chemist: Without giving a definitive quantitative answer I can say that sunburns are essentially a kind of endothermic reaction (you add energy, which makes healthy skin cells turn into damaged skin cells). Pretty much all reactions follow what's known as an Arrhenius-type rate law, which states that
r = k_0 exp( - E / RT )
where E is some energy barrier to reaction and RT (in typical chemistry) is basically the energy available to cause the reaction. What I do know about biology is that protein denaturation also follows an Arrhenius-type rate law. For a sunburn, the energy supplied is radiation energy rather than thermal energy, so we can replace RT with hf where h is Planck's constant, and f is the frequency of incoming radiation. The time it takes you to "get a sunburn" (we're really getting slowly burned all the time, but don't notice unless the burn rate is significantly higher than our healing rate) is inversely proportional to the reaction rate, so we have
t ~ (1 / r) ~ exp( E / hf ).
It's likely that what this calculator does is estimate E based on skin type and protection, and f based on the local UV-index.
Now, if you plot this function (or better, the reaction rate) and play around with the dependency on E and f, you'll find that, especially for low E (low protection) the function is extremely sensitive to the value of f (the UV-index). This means that if the calculator has a small error in the estimated UV-intensity, that can propagate to a huge error in the estimated "time until sunburn". Furthermore, the function is also extremely sensitive to the value of E, especially at high f, so if the UV-index is high, but the calculator has a slightly wrong estimate of the effect of skin type and protection, this can have a large impact on the estimated exposure time.
TLDR; It's likely that the calculator is based on an Arrhenius-type rate law. This model is, under certain conditions, very sensitive to the two input parameters (skin type / protection level and UV-intensity). Therefore, small errors in the input parameters can cause the model to give estimates that are very far off reality under those conditions.