Is there anything wrong with rubbing a stick of butter on the pan?
It would depend on how quickly you use the butter, how thoroughly the pan was cleaned, and how long the pan was stored between uses/washes, and how clean your hands were when rubbing the butter in the pan. The more contaminates you introduce the butter and the longer you store it, the more likely the butter will spoil.

Refrigerated butter is good for about a month after the sell-by date. Generally, butter that has been handled loses half its shelf life or more (generally succumbing to mould infestation). 

If your hands and pan are clean, the risk is greatly reduced. Despite this, I find handled butter's shelf life is much lower than sealed butter (1-2 weeks versus 3-4).