And I challenge the caster level bit.

Spell slots are tied to class level, not caster level.

Items that boost caster level do not add slots.

Temporary negative levels ("energy drain"?) explicitly do remove spell slots, but not in a way consistent with interpreting the quoted rules as requiring minimum caster levels to cast spells.

The quoted rules seem best interpreted as, "casters may not voluntarily lower their caster level below the minimum class level at which they receive slots with which to cast the spell".