HMP,
So you have personally looked through Key Lime's entire op specs and found they are not allowed to have SICs? I think if that was the case the FAA would be all over them like white on rice. Key Lime would not be advertising the FO program if it was not legitimate. rickair7777 is right about the 135 and 91 rules. Whenever I have an SIC on my 99, and we get a 91 leg, I usually give the leg to the FO because then they can legally log PIC time. Just food for thought...
fly safe