Anybody who says that a trainee could/should have stepped in doesn't understand how the system works. A trainee has no more authority to control on his own than Joe Blow off the street. All training is done on the instructor's license. It's not even a matter of whether or not the trainee could handle giving the clearance and clearing people to takeoff/land -- one imagines that this wouldn't pose much of a problem. It's more of a case of what happens if something goes wrong. As an unlicensed trainee who technically shouldn't even be transmitting on the frequency at all without the OJI monitoring, what do you think is going to happen if one of these guys flicks in (even if it had nothing to do with anything the trainee said)? Do you want the possibility of being held personally liable or even being prosecuted for controlling without a license (I can't see the FAA stepping up and backing the trainee in such a situation)?
If somebody did declare an emergency, that's probably the last time you'd want an unmonitored trainee trying to handle things. What the trainee would do in that scenario would be to run like hell to the bathroom to get his instructor back, then (possibly) help with calling other people in while the instructor handled the comms.
As for the Lifeguard issue, it looks to me like it was a departure, not an arrival. Nobody would go to the bathroom if there was a Lifeguard inbound. And I'm quite sure that the controller wouldn't have gone to the can if there had been any indication that the aircraft was gearing up to go imminently. The problem is that even the pilots don't know when exactly when they're going to depart because it's all contingent on the organs/patient arriving. The tower may very well have had a pending strip on the departure for several hours (this happens every single day at my facility), during which the aircraft sat on the ramp waiting for the goods to arrive. Things move quickly once these kinds of flights are ready to go, but nobody really knows when that's going to happen, and in the meantime it's not realistic for somebody to go 3 hours without a bathroom break because there *might* be a Lifeguard wanting to go in the 2 minutes it would take to get there and back.
Had I been in the trainee's shoes, depending on what the local procedures are at his facility, I might have suggested that the Lifeguard try calling the TRACON directly (assuming frequency coverage permits) to get a release directly from them. At least where I work, there's a provision where if a tower is single-manned and the controller has to take a break for whatever reason, the airspace can revert to Class E and be treated like an uncontrolled airport, and the tower frequency becomes the MF/UNICOM (basically the same thing that happens when the tower closes for the night). This would give the TRACON the authority to issue a clearance and IFR release to the Lifeguard, which obviously makes a hell of a lot more sense than waiting 10 minutes. But it's quite possible that things are different down there, which would explain why they had to hold two arrivals rather than clearing them in one-by-one (which they could have done in a Class E scenario).
But as for actually controlling, hell no. Aside from the liability questions, it would be very difficult to sort out with the TRACON since the OJI had apparently already told them to hold everybody while he went to the bathroom. Now all of a sudden the trainee calls up and tells them he's got one taxiing for departure, but no, the arrivals still can't come in -- that would be a great "WTF" moment.