Although it doesn't specifically state that you can't be both, it's pretty heavily implied. To be both fatigued and exhausted would be redundant in almost all senses, both the literal (as in describing to someone that you were both fatigued and exhausted) and mechanically, since exhausted basically does the same thing as fatigued only to a greater scale and with the added speed penalty.

Look at frightened, shaken, and panicked. It doesn't specifically say that you can't be all 3 at once, but it's heavily implied when it says that one is a more or less severe form of the other. We take for granted that someone can't be both frightened and panicked, cuz each effect does the same thing in lesser or greater degrees, occurs in the same situations, etc., etc.

Situations that cause someone to become fatigued, frightened, etc., are frequently going to beget more fear/fatigue, either as the effect of a spell or supernatural ability that an enemy really likes using or as a result of your class' abilities. To make it so you have to apply multiple conditional modifiers that are essentially the same effects is sloppy game design, and it seems very out-of-line with Pathfinder's general style of design, which is to streamline and prune back when appropriate to make battles flow more fluidly.

The better design in that case would be to create a 3rd condition where the penalties of both fatigue and exhaustion stack. Obviously the conditions are related, or one would not lead to the other, and losing one would not regress to the other. With a 3rd condition, you don't have to double your math.

You're assuming a little too little. I mean, under exhausted, it says "After 1 hour of complete rest, an exhausted character becomes fatigued." It never says you stop being exhausted, but it'd be really silly if suddenly you had more penalties for resting when you're exhausted. In the same sense, I think we have to apply the reverse. Just because it doesn't say that we stop being fatigued when we become exhausted, it's reasonable to assume so.