First, pursuant to 14 CFR Part 135.109, "[e]ach certificate holder shall designate a (1) Pilot in command for each flight; and (2) second in command for each flight requiring two pilots." Stating the obvious, if the Chief Pilot is designated as the Second in Command, then in theory that individual would be subordiante to the assigned PIC.
Second, a Chief Pilot should have demonstrated the ability, knowledge, responsibility, authority, to assume any assigned position. Since the facts are not fully known, is the Chief Pilot assigned as the SIC because said pilot isn't PIC qualified for the a/c? For example, a 14 CFR Part 135 Certificate holder may have MANY different a/c on th ecertificate; the CP does not need to be checked out in each and every a/c on the certificate. As such, it would be reasonable that the CP is assigned pursuant to the regs as the SIC.
In the alternative, is the CP training/observing/assisting helping the PIC "get up to speed" while building valuable PIC Turbojet time?
Finally, the PIC does have final authority, but it would be extremely unwise to deny input from others. Just because one is listed as PIC, that pilot isn't always the all-knowing, highest time, most experienced individual; however, the PIC would be the one the FAA has on the hook.
Communication is key and if one has an issue with the assignment of the PIC/SIC, then perhaps flying as SIC to alleviate any possible conflicts is an alternative (if you are worried about conflicts in this arena, then I believe there are bigger issues).