It's not a case of specific > general because the multiclass rules don't conflict with the hybrid rules. The multiclass feats simply allow you to swap powers; they don't say anything about overriding the hybrid rules, so they don't.
I'm not sure I understand this logic. You can take the feat - you meet all the prerequisites. Therefore you should do what the (specific) feat tells you to do, which is swap a power.
The fact that the (general) hybrid rules say you can't is a conflict. It's resolved by specific > general - the feat wins.