Do all serial ports on an Arduino MEGA 2560 have the potential to "brick" attached items when being flashed?
In the Sparkfun example the Arduino Uno is used. The Uno has only one hardware serial port, and that is used to upload a sketch and for the serial monitor. Pin 0 (RX) and pin 1 (TX) can be overriden for something else. However, then you must know what you are doing, and connect and disconnect modules as required.

The Arduino Leonardo and (Pro) Micro use a USB CDC implementation and have a unused hardware serial port at pin 0 and 1.

The Arduino Mega 2560 uses the hardware serial port at pin 0 and 1 to upload a sketch, just as the Uno. However, the three other hardware serial ports are not used, and you are free to use them.

If you use an unused hardware serial port for the OBD-II, there is no risk at all. You can use that port and nothing else messes with that port.

If you use a serial port that is also used to upload a sketch, or a software implementation of a serial port, you probably are going to make a mistake some day, and there is a risk to send the wrong data to the wrong hardware. 

[ADDED]
I see that the example code in the SparkfunHookup Guide uses the Arduino Uno and SoftwareSerial on pin 2 and 3. That is independent of the hardware serial port. The SoftwareSerial is something that should be used as a last resort, since it almost completely takes over the Arduino board. It's good to have SoftwareSerial, but try to avoid it.
If you do want to use an Arduino Uno, perhaps the AltSoftSerial can be used. The AltSoftSerial works okay for 9600 baud as long as no other code uses too much time in interrupts and no one else uses TIMER1.