Your description of the wire functions is correct.

The sensor is grounded through the exhaust, which is grounded to the engine, and from there to the battery. Some late model vehicles that have O2 sensors farther downstream (with a few more exhaust gaskets between themselves and the engine) have a supplimental ground wire for the exact reason that you mentioned. These sensors are easily identified since there are 4 wires leaving the back of the sensor, and with close inspection you will notice that one is attached to the sensor shield jacket (sensor housing).

If I'm watching the O2 sensor voltage with the engine running, I probe the connection on the green wire where it couples to the vehicle wiring harness(without disconnecting it) and watch how many volts it produces (with reference to the negative terminal on the battery). If you unplug your O2 sensor, the car will assume that it's running lean and enrichen the mixture to try and produce the desired results from your O2 sensor. (since it doesn't know it's disconnected)

Of note, if your O2 sensor is bad (loosing calibration), it will read fewer volts than it should. The car will interpret this data as running lean, and enrichen the mixture until the desired output is reached. You may see the proper voltage from the sensor, but without an exhaust gas analyzer, there's no way to see if it's truely working within spec. Therefore, for optimum fuel economy, it's advisable to replace the sensor every 5 years. You can obtain a cheap 3-wire Bosch sensor (13913 or 13953) if you're willing to cut and crimp a few wires. More info in this post: (click here)

God bless,
Fitz Fitzgerald.
--
'87 Blue 240 Wagon, 246k miles.
'88 Black 780, PRV-6, 145k miles.