"For example, I had never before seen a 1:1 transformer! I just assumed transformers were for changing the voltage; I have no idea what he was trying to accomplish."
That sounds like an "Isolation Transformer":
From Wikipedia, the free encyclopedia
An isolation transformer is a transformer, often with symmetrical windings, which is used to decouple two circuits. An isolation transformer allows an AC signal or power to be taken from one device and fed into another without electrically connecting the two circuits. Isolation transformers block transmission of DC signals from one circuit to the other, but allow AC signals to pass. They also block interference caused by ground loops. Isolation transformers with electrostatic shields are used for power supplies for sensitive equipment such as computers or laboratory instruments.
In electronics testing, troubleshooting and servicing, an isolation transformer is a 1:1 power transformer which is used as a safety precaution. Since the neutral wire of an outlet is directly connected to ground, grounded objects near the device under test (desk, lamp, concrete floor, oscilloscope ground lead, etc.) may be at a hazardous potential difference with respect to that device. By using an isolation transformer, the bonding is eliminated, and the shock hazard is entirely contained within the device.
In a pinch, a line-voltage isolation transformer may be made by determining the total load of the device under test and finding two identical line transformers each capable of handling the load. A power cord is attached to the primary of one transformer, an outlet to the primary of the other transformer. The secondaries are then connected to each other. An example with two 120 V:12 V transformers would yield 120 V → 12 V → 12 V → 120 V.
Isolation transformers are commonly designed with careful attention to capacitive coupling between the two windings. This is necessary because excessive capacitance could also couple AC current from the primary to the secondary. A grounded shield is commonly interposed between the primary and the secondary. Any remaining capacitive coupling between the secondary and ground simply causes the secondary to become balanced about the ground potential."