I've had two Painkillers (camo and black covers), and I did notice that both of them were more prone to feedback than any other pickups I've owned. I didn't find it necessarily a bad thing, as it was pretty useful at times and wasn't hard to control, so it was just something to keep in mind, but I can see how someone would find it annoying.
I'm not entirely sure what you can do to resolve it, as I'm not totally sure what's causing it. Unless yours is worse than mine was, I don't think it'd be a problem with the potting (as it's unlikely so many aren't potted correctly, knowing BKP's standards), so I'm thinking maybe it's just a function of the resonant frequency of the pickup being particularly "peaky". I found rolling off the tone pot helped a little, and rolling off the volume pot helped a bit, too, and keeping my hand on the strings or not facing the speaker helped a lot more, but they're not exactly ideal solutions.