It sounds like the 135 operation in question only has one aircraft. Based on if that is the case I think it really depends on how the "exclusive" lease agreement required by the FAA is setup between the owner and the 135 company. Is it a LLC (leasing company) that did not pay sales tax on the aircraft that owns the aircraft and is leasing the airplane exclusively to the 135 operation who is paying the owner back an hourly rate plus sales tax. If that is the case than technically the airplane is going to be operated by the 135 operation and the owner will more than likely be paying the 135 operation to operate the aircraft and pay the 135 operation for the use of pilot. In this case the aircraft would not be operated under part 91 rules and would be considered a charter flight even though the aircraft is technically owned by the passenger. This is a very grey area and more than likely the FAA would not enforce it but they could.
On the other hand if the operator operates multiple aircraft and has a non exclusive lease with the owner than there would be no issue with the owner using his airplane and contracting the pilot services through the operator. This would be a part 91 flight using a typical 91 management agreement. As previously stated after a 91 flight operated by the owner a 135 MX validation would be required. The only legs that require a 135 crew are those that are 135 legs. Technically you can exceed your flight time limitations as an example as long as it is on the last leg and a dh leg because you are now operating under part 91 rules which is not subject to duty flight time limitations.
I think the key issue that distinguishes this from most other situations is that the charter operator only has one aircraft and is required to have an exclusive lease in place. (Or legally should as per OpsSpec A008.)