Quick Answer
Here's a quick answer to your question. YES. If you are flying an IFR, 135 passenger-carrying flight, the operator is required to have 2 pilots by regulation. At the discretion of the operator, they can apply for and be approved to operate single-pilot with an autopilot. This is an option that can be excercised but does not require the operator to. It's an available option. The required SIC would have to be trained and with the proper 135 and employment documentation to be the SIC. The SIC would have to have completed the requirements of part 61. (3 t/o and landings, CRM, single-engine work...) If you have a turbine powered aircraft with more than 6 pax seats and fly with a required SIC, you've gotta have the CVR.
There are not a lot of part 91 situations which would require an SIC unless the aircraft was certified for 2 pilots. Lots of part 25 jets and bigger turboprops (>12,500#)
can be flown single pilot if desired but just because you have a single pilot authorization or type-rating, doesn't mean it has to be flown without an SIC.
Insurance or company policy requiring an SIC is not a legal reason to log SIC. It must be required by certification or the rules under which the flight is flown.
I flew SIC in a King Air 300 (>12,500#) because the Captain's type stated, "SIC Required". This was all part 91. A single pilot Cessna 501 or 525 or whatever is flown single pilot a lot, but if an SIC meets the requirements of part 61.55, the single pilot authorization can be set aside and the aircraft can be flown with an SIC. It's important too, that the PIC meets the annual proficiency check of an aircraft requiring more than 1 pilot versus the biennial requirement if he or she simply flew it single pilot. (Regardless of what the insurance company requires)
Sorry, it wasn't a very quick answer but I believe this should clear things up a little.
-PJ