First of all, the insurance company requirements have NOTHING to do with a SIC being able to log or not log time. It's an insurance requirement, not FAA. If your company is like 99% of 135 charter operators, your OPSPECS are probably setup such that an autopilot may be used in lieu of a SIC for pax ops. That does not mean that an SIC cannot be used. It just means if your company chooses to operate with the autopilot instead of the SIC, they're allowed to. They do NOT have to operate without the SIC though. Here's a link to the Letter of Authorization from the FAA Chief Counsel's office:
Ok, onto the manipulation of flight controls on a 135 flight:
Regardless of what (or what you think) your POI says, this is actually quite clear looking at the regs. First of all, let's look at who can manipulate the flight controls under a part 135 flight:
Sec. 135.115 - Manipulation of controls.
No pilot in command may allow any person to manipulate the flight controls of an aircraft during flight conducted under this part, nor may any person manipulate the controls during such flight unless that person is --
(a) A pilot employed by the certificate holder and qualified in the aircraft; or
(b) An authorized safety representative of the Administrator who has the permission of the pilot in command, is qualified in the aircraft, and is checking flight operations.
In your own words, you are saying your company chooses to operate 135 flights under the single pilot authorization, and that the 2nd "pilot" is not required. So in other words, you (or whoever the "SIC" is) are considered a passenger. A passenger is not permitted to manipulate the flight controls as stated in FAR 135.115 above.
I think you were a little confused and did not mean to say that you guys choose to operate under the single pilot authorization when you are sitting in the right seat. In other words, you want to be classified under 135.115(a) as a pilot employed by the company and qualified in the aircraft. So what constitutes you (the SIC) being qualified in the aircraft? This is where FAR 135.293 comes into play:
Sec. 135.293 - Initial and recurrent pilot testing requirements.
(a) No certificate holder may use a pilot, nor may any person serve as a pilot, unless, since the beginning of the 12th calendar month before that service, that pilot has passed a written or oral test, given by the Administrator or an authorized check pilot, on that pilot's knowledge in the following areas --
(1) The appropriate provisions of parts 61, 91, and 135 of this chapter and the operations specifications and the manual of the certificate holder;
(2) For each type of aircraft to be flown by the pilot, the aircraft powerplant, major components and systems, major appliances, performance and operating limitations, standard and emergency operating procedures, and the contents of the approved Aircraft Flight Manual or equivalent, as applicable;
(3) For each type of aircraft to be flown by the pilot, the method of determining compliance with weight and balance limitations for takeoff, landing and en route operations;
(4) Navigation and use of air navigation aids appropriate to the operation or pilot authorization, including, when applicable, instrument approach facilities and procedures;
(5) Air traffic control procedures, including IFR procedures when applicable;
(6) Meteorology in general, including the principles of frontal systems, icing, fog, thunderstorms, and windshear, and, if appropriate for the operation of the certificate holder, high altitude weather;
(7) Procedures for --
(i) Recognizing and avoiding severe weather situations;
(ii) Escaping from severe weather situations, in case of inadvertent encounters, including low-altitude windshear (except that rotorcraft pilots are not required to be tested on escaping from low-altitude windshear); and
(iii) Operating in or near thunderstorms (including best penetrating altitudes), turbulent air (including clear air turbulence), icing, hail, and other potentially hazardous meteorological conditions; and
(8) New equipment, procedures, or techniques, as appropriate.
(b) No certificate holder may use a pilot, nor may any person serve as a pilot, in any aircraft unless, since the beginning of the 12th calendar month before that service, that pilot has passed a competency check given by the Administrator or an authorized check pilot in that class of aircraft, if single-engine airplane other than turbojet, or that type of aircraft, if helicopter, multiengine airplane, or turbojet airplane, to determine the pilot's competence in practical skills and techniques in that aircraft or class of aircraft.
The extent of the competency check shall be determined by the Administrator or authorized check pilot conducting the competency check. The competency check may include any of the maneuvers and procedures currently required for the original issuance of the particular pilot certificate required for the operations authorized and appropriate to the category, class and type of aircraft involved. For the purposes of this paragraph, type, as to an airplane, means any one of a group of airplanes determined by the Administrator to have a similar means of propulsion, the same manufacturer, and no significantly different handling or flight characteristics. For the purposes of this paragraph, type, as to a helicopter, means a basic make and model.
(c) The instrument proficiency check required by §135.297
may be substituted for the competency check required by this section for the type of aircraft used in the check.
(d) For the purpose of this part, competent performance of a procedure or maneuver by a person to be used as a pilot requires that the pilot be the obvious master of the aircraft, with the successful outcome of the maneuver never in doubt.
(e) The Administrator or authorized check pilot certifies the competency of each pilot who passes the knowledge or flight check in the certificate holder's pilot records.
(f) Portions of a required competency check may be given in an aircraft simulator or other appropriate training device, if approved by the Administrator.
In other words, to act as a qualified pilot that can manipulate the controls under part 135, you must be given a check ride that includes an oral and practical test. This check ride must be given by the FAA or a designated check airman (usually the chief pilot has this authorization). It does not differentiate between PIC or SIC - it is REQUIRED for any pilot. This is very common knowledge in the charter world, so you better check into it.