You can do lookup on all IP addresses. To find out who owns or is registered to what blocks.
You can look up the domain names to registrars, find out who is assigned to what IP.
Each user who logs into these p2p apps most likley are either having a reverse lookup performed on them each time they log in (like IRC), then those logs are scanned over, with scripts to locate known names of these associations, such as BMG, ASCAP.
Then when the flags are signaled, they can just assign a whole block of IPs to be banned , for example if a flag was signaled on the ip address of 127.0.0.3 you could ban it, or ban a whole block easily, 127.0.0.3/24
The practice is not a guarantee, as those companys can easily register/purchase a whole new block of ips that are not presently banned.
This is not 'piece of mind'.
IP addresses change often.
If you want to understand it better, look up some books on TCP/IP networking.