When you state that the insurance company are happy to include you I presume that this is either as a named pilot or that you fall within the acceptable criteria that they have laid down under an open pilot warranty.
If this is the case then there is no reason why they would not pay a claim so long as you are only using the aircraft for a permitted purpose. If you are only paying the direct fuel costs then I would have thought this falls under the 'contribution to the direct costs of the flight otherwise payable by the pilot in command' definition.
Is there anything in particular that makes you worry you would not be covered?