So how exactly does one fit that need for privacy into the schedule and mission?
What I'd do is unplug the cameras whenever I didn't want them on. Of course I wouldn't tell them that before launch, but it only makes sense. Being several years away from a rescue team, there's no way I'd be wasting limited resources operating a camera if it wasn't necessary for the task at hand, and It's not like mission control could do anything about it. I'd be so far away that it's impossible to hold a real-time conversation, and it's designed as a one-way trip. It's not like they could fire me or punish me with anything more than a strongly worded email or nasty phone message from that distance.
It's a technically simple problem, but a logistical nightmare during an emergency situation.
It would take either a massive government subsidy to get it done, or your cell phone bill would skyrocket to cover the additional infrastructure costs.