It's not a scam, it's just the way ASACAP/BMI work. They are legit, even if their tactics are shady and misleading and possibly illegal. Brett had the right idea. As much as I'd hate to give in to these guys, they're very hard to fight. You can try blowing them off, but eventually it might come to a court battle. For what they want you to pay, it's easier just to pay the fee and then you have the right to play any music they license, not just the royalty free stuff you've obtained. The venue I worked at decided not to fight them and just pay the fees. We even stopped our "rave" nights since the DJ royalties were much higher. And the real kicker, they charged us as a food and drink establishment and not a concert venue, because as they said, we don't have permanent seats so that's the category they claim we fall into. Sure we could have fought it, but you're looking at a lengthy legal battle with a company who has some very high priced lawyers.
Funny, you wouldn't think a non-profit who is supposed to be helping musicians get the royalties they're due would become known for such ruthless tactics. In the end they do pay out to the musicians though, but they sure do leave plenty of money to pay their lawyers.