My interpretation of the entry:
Spells: Driders may be 6th-level clerics, wizards, or sorcerers.
...was that they get the spells/day and caster level of a 6th level cleric, wizard, or sorcerer, and since it specifically indicates "spells", that it meant that no other abilities of said class.
Plus, the monster statblock does not mention the possible special abilities of Turn/Rebuke Undead, Summon Familiar, or Scribe Scroll, nor does it instruct to select an extra metamagic feat (in the case of a Wizard, they would gain one at 5th level). So, I've basically assumed that while spellcasting is equal to a caster of said level, that all other special abilities must be learned.
I know that technically, a drider is created from a pre-existing drow character of the appropriate class and level, and should have said abilities. Yet, if they had intended for the drow to keep them upon transformation, they probably should've made it a template. As a monster statblock, it's just easier to take the drider as-is and tack the appropriate spellcasting levels on, than it is to massage it into having PC levels of the appropriate amount, complete with all feats, special abilities, and companions.