So I would like to comment on this 🙂
Urine is indeed sterile...before it exits your body. However, lets take a deeper look here. Each of us has what is called "Normal Flora" - These are organisms that are normal to "us". So urine is sterile only in a personal sense. For example - if you have a urinary tract infection, your urine carries all those things that would make your skin crawl if you saw it under a microscope. Is it sterile? Yes - because it has not left your body yet.
Urine stile carries everything we don't need. So if you have a pee rag, and you leave it on your bag - the no longer sterile urine will touch things that it comes in contact with.
How many of us has seen a "pee rag" that has fallen off on trail? You ask yourself when you see that hanky "is it...or is it not?" The good hiker would pick it up - for conservation and for courtesy. However a pee rag lost on trail is just as bad as dropping food and/or anything else.
If you use a pee rag - make sure it is secure...and wipe that bag when you get off trail...or that pee of yours will be on every single trip there after!