It could count. You have to be afforded the 10hrs of rest. I don't think this necessarily means that the company has to pay for a hotel room, but you have to have the opportunity to rest 10 hours as in being able to sleep if you desire, before resuming duty. If the situation is such that it's not practically possible, then you're not afforded that rest. You are not "required" to rest during that period. There are many FAA legal opinions on this that reinforce many common themes. You can search for them on the FAA's DRS system. They recently moved the legal opinions to the AGC tab down on the left side and the search function is pretty clunky to use, but 135.267 comes up many times. I don't think we have enough information to decide if it does or does not count.