Are Knowledge skill checks Charisma-based after the Lore Keeper Revelation?

Question

Lore Oracles can take a Revelation called Lore Keeper:

Lore Keeper (Ex): Instead of encyclopedic knowledge, you learn most of your information through tales, songs, and poems. You may use your Charisma modifier instead of your Intelligence modifier on all Knowledge checks.

They also have access to a Revelation called Focused Trance (emphasis mine):

Focused Trance (Ex): You can enter a deep meditation, blocking out visual and auditory stimuli and allowing you to concentrate on a single problem, philosophical issue, or memory. This trance lasts 1d6 rounds, during which time you can only take move actions. During this period, you gain a bonus equal to your level on all saves against sonic effects and gaze attacks. When you come out of your trance, you may make a single Intelligence-based skill check with a +20 circumstance bonus. You may enter your focused trance a number of times per day equal to your Charisma modifier.

If a Lore Oracle has both of these Revelations, can they use Focused Trance to add the circumstance bonus to a Knowledge check, or is the Knowledge check now a Charisma-based skill check?

Answer 1

No.

They are still Intelligence-based skill checks. You simply have the option to use your charisma bonus instead of your intelligence bonus.

If, for whatever reason, like being drained of your charisma, you must make a Knowledge check, you can still use your intelligence bonus.

However, if you decide to use Focused Trance, you will have to use your Intelligence modifier instead of your Charisma modifier, as that changes the ability that the skill is based on at the time of the roll. Otherwise you cannot gain the +20 bonus from it.

If you decide to use your Charisma bonus on a Knowledge check, that check is now Charisma-based. The skill remains as Intelligence-based though.