If the company requires the trip, then it's duty. If you're approaching your rest limits (which, while Part 135 doesn't prescribe duty limits, still equates to your 14 hours of duty), then the company can't assign duty (and you can't accept duty) that puts you beyond your rest limits--10 consecutive hours in the previous 24.
If you've already put in your 14 hours and you have a reposition flight, you can do it if you volunteer...if you want to do it, fine. The company can't ask or assign you to do it. This is a key issue.
The rest of the post was good, but this is not correct.
Duty and the duty day don't exist. The issue is when accepting a Part 135 leg can you look back over the appropriate periods and find the required rest. Anytime you are working for the company, flying, cleaning toilets, doing paperwork, training, cleaning the aircraft, is NOT REST, and you can call that duty if you want, but you'd be wrong, but the only thing we know is it is NOT REST and so it cannot be considered when trying to find lookback rest.
So the whole concept of "it's duty" and "you can't exceed some mythical 14 hour limit Part 91" is not correct. You cannot be scheduled for Part 135 flying that exceeds 14 hours, but we've agreed this is Part 91 flying. No lookback to find required rest is required, you're always good to go.
You work for the company, the company can tell you what to do regardless of Part 135 flying, Part 91 flying, toilet cleaning, paperwork etc. The concept that you cannot be assigned Part 91 flying is bogus and has no basis in flight regulations. Any basis at all on what you can be told to do would be labor laws, and labor laws know nothing about rest and duty.
You can work Part 135 flights, you can extend the 14 hour "duty day" as long as needed for unexpected delays and you can still be assigned a Part 91 flight leg at the end of it all. Under the regulations you can decline that leg as fatigued, just as you can decline ANY leg as fatigued and the FAA expects professional pilots to do just that. How that works out between you and the company employment-wise is a whole different issue and the FAA could care less. This is flight and duty time regulations, the FAA doesn't regulate labor and as a courtesy the Dept. of Labor doesn't regulate flight time.
There are a number of FAA opinions on Part 91 legs, and they all pretty much say the same thing. Part 91, at the end of Part 135/121 flying can be done for as long you want. It's not relevant to duty periods or rest periods or anything. Going forward it IS commercial flying and has to be counted on any subsequent lookbacks and it is NOT REST and cannot be counted as such.