You missed the example in my post, 5 for fireball is for a wizard, it'd be 6 for the Sorc, because he gets spells later that's his minimum.
I said right there in the post that the minimum level for the spell to be cast is dependent on the class casting it not the spell it self.
If your class gives you spells at a different progression it will change what your minimum caster level is, lets take remove curse as an example.
So for a Bard 7th, a Cleric 5th, a Paladin 5th, Sorc 8th, Wiz 7.Level: Brd 3, Clr 3, Pal 3, Sor/Wiz 4
Same spell, different minimum caster level for each class.