That only applies to the legal system. Rightscorp is bypassing the legal system and instead getting the ISPs to do the work of law enforcement, and with no analogue to the court system. Basically there are three private parties, Rightscorp, the ISP, and the ISP's customer, and any of the three is legally allowed to presume the other two parties are guilty bastards without proof. Also any of the three are able to sue if they feel unfairly treated if they think some laws are being broken, and they can countersue if anyone sues them, if they'd rather spend that kind of money doing so.
Well, Alrighty Then! You just stumbled on the solution.
Since (I assume) no agreement exists between Rightscorp and the ISPs, said ISPs can (and should) simply tell Rightscorp to POUND SAND, because they are simply not under any statutory nor contractual obligation to even READ Rightscorp's request; let alone HONOR it.
Bottom line: If Rightscorp wants to take alleged "infringers" to court, they have to do it the "right" way (i.e., through the DMCA).
They simply cannot turn ISPs into Police, Judge and Jury, at least not in the USA.
INAL, but AFIK, even in civil cases, there are still a modicum of Due Process Rights that one has. Yes, I know this isn't in a Court; but I'm about to change that...
Every single alleged infringer needs to file a Small Claims Court case against their ISP and Rightscorp, suing for the statutory maximum (usually $5k to $10k). It only costs about $50 in most jurisdictions, and in most jurisdictions, corporations MUST hire an attorney (there goes a minimum of about $2500 for them).
Better yet, If you file in regular (Superior or Circuit) Court in your Jurisdiction, it costs a little more (usually around $100-200), but then, the Corporation MUST hire an attorney (while you can ALWAYS represent yourself "pro se"). In both cases, your meme is going to be "extortion", due process violations, and "frivolous and vexatious litigation". Also throw the words "professional misconduct" around.
Speaking of which, while you're at it, when they DO retain an attorney, then write up a "Grievance" to their local Licensing Board (often the Supreme Court in the State they are practicing), alleging Professional Misconduct (attorneys cannot advance frivolous claims), and that you have Standing to do so even though it isn't your attorney, because your Grievance is based on the "Proper Administration of Justice" and because every Attorney is an "Officer of the Court" FIRST, and MUST uphold their Jurisdiction's Rules of Professional Conduct for Attorneys (you can find them online on your State's website), EVEN ABOVE their duty to "zealously defend their client".
Even if the Licensing Board doesn't formally start a Professional Conduct procedure against the law firm (which they won't), said law firm/attorney HAS to inform their Malpractice Insurance Carrier of the Grievance, which can cause them to be dropped by their carrier, or at least, pay increased insurance rates. Most states also list on their Roll of Attorneys how many Grievances have been filed against them, which can limit their future business, and possibly affect their local Bar Association's "Rating" for them.
IOW, since they are playing fast and loose with the concept of "Justice", you can play "Hardball" with the tools at your disposal, too. All it takes is a few hours of research and typing.
To quote a great line from "Boston Legal": "I like to put the Adversary back into the Adversarial Process."