I sometimes make my own, and often use Sweet Baby Ray's right from the bottle.
I also take commercial sauces and add things to it to make a new sauce. I like to add heat and sweet to my commercial sauces. Take any store sauce, and add honey and black and/or cayenne pepper to it. I love it.
If you use a commercial sauce right out of the bottle, then you need to leave the label on it, or put it in an unmarked bottle -- you may prefer a squeeze bottle to the glass bottle, and a plastic bottle is definitely safer. That is a legitimate and practical reason to use a bottle that does not have the maker's label on it. IMO. I would never do it just to make people think I made it.
If you doctor it up, I think it would certainly be okay to put it in an unmarked bottle, but I still would not put any kind of label on it that leads people to think that it is your own.
The only way I would put a label on it that people would take to believe that you made it, is if you actually did make it, from scratch.