Terminal sometimes scrambles initial output
I would like to answer my own question, even though it is not an "answer," per se.

After testing on several different machines, I am confident that this is a bug with Terminal (and perhaps other virtual terminals on other operating systems). I have tested this on the following machines that are owned by separate users:


MacBook Pro (2012, 13-inch) running 10.9.4
MacBook Air (2012) running 10.9.3
MacBook Pro (2012, 15-inch) running 10.9.4


If someone would like to add to my list, please try running Terminal and quitting it in succession until you see the timestamp located on the same line as the initial prompt.

A friend of mine claims to have seen this on Linux as well.