Correct me if I'm wrong, but what I am taking away from this is that I shouldn't even be trying to use the TX and RX pins as outlets for transferring data because its proper use is for applications involving an arduino board and a PC or USB.
You are wrong there. If you aren't using the USB/Serial to connect to a computer, then there is no problem using the TX/RX pins for serial communication to another device. All that is saying is that the LEDs won't blink under those circumstances.