I would side with the Boss....you get your Ten Hours Rest.....accepted no Flight Duties (you are flying as a passenger with no duty imposed).
The only quiestion would be if there is a penalty (extended Rest Period due to the extended Duty Period) prior to the start of your next Duty period.
The key issue is the difference between "Duty Hours" and "Flight Duty".
Read your Part 135 very carefully....and consider every bit of the wording used in the Regulation.
The "nuance" in the language is key.
FAR 135.267 pertains but care must be taken to ensure which part of it covers your particular operation to include also considering what the OpSpecs for your particular operation have to say about the matter.