Maybe I misunderstand the legal situation here, but if "they paying someone to develop a few lines to the Linux kernel and every other project", then they would only have standing to sue regarding those specific lines right? Unless they can get other contributors on board.
Standard IANAL, but I have to deal with copyright issues sometimes.
Yes, they would only have standing to sue based on those lines and any lines based on them as a derivative work. I'd imagine that if they showed they were good custodians of suing people (making it easy to get back in compliance as opposed to trying to milk people of money) they could get people to join them on a case-by-case basis.
Even without that, they don't have to prove the value of the code that was used. You can sue for copyright infringement based on a standard damage instead, which is assumed to be 10k-250k per violation.