That cannot be it for the general case: Sorcerers also have spellcraft and knowledge(arcana) as class skill.
It should also be pointed out that this "rivalry" is something we are seeing in Rich's interpretation of the rules. The rules as written do not mention this.
I think the rivalry makes sense due to all(!) the stuff outlined above. There's a lot reasons for "academic" wizards to look down upon those arcane Rainmans (who in turn have the right to feel looked down upon).
I always saw Rich's interpretation of Wizards as elitist university professors.