Well I've installed the Service Saver maybe about 50 times and they are nice but they are generally not the safest thing in the world. Yes, you need to make sure you have two good wires, if two of three are bad, then you will have problems like someone already mentioned. You would not install one because of a bad transformer, unless you can visible see that a lug is broken externally because you have to assume that the whole thing is bad if it's faulted internally. So, either the guy didn't know what he was doing, your parents misinterpreted him, or a lug is broken externally. Usually we would hook up a generator until a new pad is ready to go in, maybe a few days at the most.
They suck because you have to jam a good amount of wire into a meter trough and in general, if the service is old, then the trough is old so you could be opening up a bigger can of worms. Plus you generally have to stick two wires under one lug which is not good.
They most likely did you parents a favor since pretty much all underground services are owned by the property owners from the property line to the house, at least here anyway. Giving them full 240 instead of making them dig on it right away if the fault was inside the property line. The other way to temp fix it, which I think is better but not always feasible is what macmikeman said above.
By the way, as someone already mentioned, The Beast is a hairdryer with a voltmeter built in, not a transformer. The actual name for the auto-transformer on the dolly is the Service Saver, we call it the 1:1 here. There are different sizes, but most of them have 80 amp main breakers so you do get 120/240 but less than half of a normal service as far as amperage.