You must meet the requirements of the feat. Like every other class ability that grants feats. According to the PRD:
Some feats have prerequisites. Your character must have the indicated ability score, class feature, feat, skill, base attack bonus, or other quality designated in order to select or use that feat.
The bolded part is a blanket rule that applies to all feats in the game, like those gained by a fighter, unless said otherwise, like on the monk and ranger classes:
A monk need not have any of the prerequisites normally required for these feats to select them.
even if he does not have the normal prerequisites.
Or when a class or ability grants you a feat as a bonus feat, the requirements are not required, as per this answer, unless the ability says the requiements must be met.
You could argue that this ability is considered a bonus feat, but the rules-as-written here says it is not. And thus, that quote from James Jacobs does not apply here.
Keep in mind that granting any feat in the game is really strong, way stronger than any of the other secrets available, as you could even get feats designed for monsters or mythic heroes if the requirements are ignored completely. Classes that grant bonus feats that ignore the requirements either specify the feat gained, or have a list of available feats (like all combat feats or style feats).