Let's say you're coding, and you come across an opportunity for simple code resuse (e.g. pulling a common piece of code out to an accessible place like a Utility class or base class). You might find yourself thinking, "I know it's good to do this, but I have to get this done now, and if I need to make a change to this code, and forget to change it in the other place, my testing framework will let me know."
In other words, you let the awesome tests you (or another developer) has written to remind you to change the code in the other places too.
Is this a legitimate problem that we might find in ourselves or other developers?
You're asking whether unit tests encourage you to rely on them as a method of TODO list? Yes, but I don't think that's sloppy coding. You are, afterall, to start with unit tests failing and code to the test; if you refactor some code and then once again code to the test, that isn't sloppy coding -- it's doing what you're supposed to.
I think the problem with unit tests is simply that you can't cover every corner case in a unit test, and sometimes people assume that a working test means a working app, which isn't true.