Explanation of class skills does not have to make perfect sense, because there is no such thing as a perfect game. But Spatula et. al. has the right idea: keep in mind that, just because you are a computer programmer, you have professional level skill to ride a bike competitively (the level of skill represented by class skills).
A better example: A rogue is naturally predisposed to Appraising the value of objects. Because of the nature of a rogue's world-wise field of study, Appraisal is something that he can not only come into contact daily, but also something that he, more so than a fighter, has the chance to practice daily. Even if the rogue doesn't spend any skill points in appraisal, he has passed up ten times as many chances to appraise goods in the field as the fighter would ever get to do.
Another anecote: Jumping and climbing come as easily to fighters and rogues as swimming does to a fish. Why is this so? Because jumping and climbing comprises half of their combat training as it is. Fighters must be mobile enough to reach their targets, or to put themselves in as advantageous a position as possible with respect to their targets. A wizard, on the other hand, has almost no opportunity to practice said jumping or climbing skills in life or death situations. Instead, they have seen the casting of THOUSANDS of spells, and has had the opportunity to observe every type of spell aura; they may have had life or death training based on how quickly they could determine an opponent's cast spell by aura so as to counterspell it.
(Now THAT's one hell of a final test from master to apprentice: "Apprentice, I am about to cast either a burning hands or a magic missile at you. YOU must decide which one, and how to counter it. If you fail, you will be dead, as these spells are REAL. Good luck to you, and Boccob keep you. If you live, the celebration party is in the next room.")
Therefore, a fighter's only exposure to spellcraft is what he can be read and taught; a wizard's exposure is through both book learning and field experience.
Thinking about it as cross-class skills being book learning, and class skills as being APPLIED book learning with LOTS of logged field time, and the distinction should become clear.
Simply put, if a fighter has logged enough field time to start easily identifying spells, he knows enough to start casting rudimentary spells, and his fighting skills start to suffer. In short, he's changed classes. Too much emphasis is placed on character classes as being like TV Channels - you make a voluntary and conscious switch from one to the other. But they are more like collegiate degree programs - if you've taken enough classes in one field, you meet the qualifications for a certain degree in that field. Take more classes, and you've earned a higher degree in that field. Take more classes than that, AND log field time in certain activities, and you earn an even HIGHER degree. Classes can be just as descriptive as proscriptive - just like alignments.