Actually, the theorem doesn't generally apply if some of the regions are disconnected. Imagine that you had three adjacent countries surrounded by a fourth, so that they are required to use four different colors. Then imagine that there is a large lake inside each country. As long as all bodies of water are required to be the same color, you will now have to use a fifth color for the body of water - "water" is basically a "country" that is disconnected and touches each of the four other countries without getting in the way of them all touching each other (which is impossible if it had to be a contiguous country).

And of course, the actual Earth has a few countries with that sort of disconnection as well, notably Congo (Kinshasa) and Russia.

Fortunately, the pattern of lakes and oceans, as well as the pattern of exclaves of Russia and Congo (and perhaps any others?) don't actually get in the way of using just four colors. But once you allow exclaves of this sort, it's easy to come up with maps that can't be colored with four colors.