Sounds like you're dealing with one of the music licensing groups (ASCAP/BMI/ect). If you were required to have a federal license to operate an amusement park (which I've never heard of being done on a federal level) then I doubt that'd charge you per head. ASCAP on the other hand will, and they will be ruthless and make whatever threats necessary. I worked at a concert venue who got hit with a $5,000 a month bill. When we tried to fight it they claimed they would start collecting the back royalties that we hadn't been paying, unless we cooperated. It's hard to fight these guys, but if you're careful it can be done. As long as you're sure you're not playing any licensed music you have something to stand on. But they will watch you, and the second you screw up they will fine you. They've been known to send "spys" to bars and clubs to see if they're playing licensed music. It's essentially a legal shakedown.
The line about requiring written permission from Virgil is bull. Unless he's with ASCAP (and I doubt they'd know in the first place) you don't need written permission. It's not the job of ASCAP to enforce ALL copyrights. They're a private organization and have no right to do so.
Expect more visits. Usually when ASCAP shows up BMI is not far behind.