UPDATE: I've been working all day trying to find what might be happening. I've identified that this issue happens every time with Apple computers running Mountain Lion. I made the exact same test I posted here on three Apple computers running Mountain Lion and got the same results on all of them.
I also tested a Ubuntu system and it worked there. I have yet to test a Windows system. My question is: What might be happening with Apple computers when running this test? Is it something to do with the USB to TTL Serial cable's driver for Mac? Would another method of establishing a soft serial connection (for example the FTDI Friend) work to perform this test on a Mac?
I wish someone would test and confirm these results. I would like to get to the bottom of this problem. Thank you very much for your time!