Just to be clear: with software like DBAN, Killdisk, or Blancco, you can indeed permanently erase data from your computer's disks, even to the point that no one - not even the NSA - could ever recover it. The problem is, they didn't have access to your computer to find out you downloaded the file. They don't NEED access to your computer if and when they do decide to file a lawsuit. They have all the evidence they would need from their end. That said, they probably would want to examine your computer to retrieve additional evidence against you.
The deletion of files from computers has been discussed in several threads in the past. Generally, if you know that a suit might be filed against you, deleting files can be a mistake. With notice of infringement, and prior to a legal action being filed, deletion may or may not be a recommended course of action. It is always wise to discuss deleting files with an attorney prior to acting, so the attorney can review the facts and the history of the copyright holder. Sometimes deletion is all that a copyright holder wants.
See the following threads previously posted on this forum about "spoliation of evidence" and what erasing data from a computer disk can show:
https://forum.freeadvice.com/arrests-searches-warrants-procedure-26/spoliation-evidence-557249.html
https://forum.freeadvice.com/online-purchases-sales-87/recieved-subpoena-563646.html
A computer forensic expert's examination of a defendant's computer is frequently a part of discovery in any online infringement action.
What these operations do is sit on the other end of a torrent file (they actually help share the file) and watch who connects to them to download it. They then send out $250 payment demands to the owner of every IP address that connects to them and downloads the files. This is the culmination of efforts originally begun by Sony, who started seeding defective files into the P2P libraries around 1999. So far, these companies' sharing of their own copyrighted works (or the works of those they represent, with permission) then suing end users who take advantage of those works has stood up in court.
I agree that the tracking of copyrighted material to a downloader's computer is usually enough evidence to support, and win, an infringement suit. There are arguments that can made in defense of an infringement suit if this is ALL of the evidence against a defendant, however.
I foresee legislation at some point similar to the FDCPA that would disallow the practice of threatening a lawsuit when one has no intention of bringing said lawsuit. These trolls just send out as many letters as they can and hope for the $250 checks to roll in. Their MO is no different than a few Nigerian princes I'm familiar with, other than that they usually have an actual lawful basis for a complaint if you were to antagonize them.
What has been discussed, and what is happening already in many cases, is that the notices will be sent by the copyright holder (or the attorney or firm representing the copyright holder) to the ISPs and the ISP will inform the account holder that an illegal download has been tracked to their account. It often will end there if the account holder deletes the file and does not infringe again. Unless the infringement continues, the copyright holder will not pursue legal action and the ISP will not terminate the infringer's account.
That said, the settlement letters demanding compensation can continue and a subpoena can be issued for account information. It is the right of the copyright holder to be compensated for any unauthorized and illegal use of their copyrighted material. In other words, it can be a risk for the infringer to completely ignore a demand letter from most copyright holders, because a lawsuit can result and an award of damages stands to be far greater than the amount demanded prior to suit.
The lowest amount a court will order in damages is $200 (at the discretion of the court and only if the infringement is shown to be "innocent"). Otherwise, an infringer can expect to pay damages from between $750 and $30,000, should the copyright holder take the infringer to court (with an award of statutory damages often in $2500 to $5000 range plus attorney costs).
Because there is a legitimate legal action available to pursue by a (legitimate) copyright holder if their copyrighted work is infringed, neither the settlement demand letters nor the threat of or the filing of a lawsuit can be viewed as a scam or as extortion (unless, of course, the demand letter or suit is filed by someone without standing to sue). Sometimes it is advised to settle, if you know you have infringed and there are indications the copyright holder will take further legal action if payment of the demanded figure is not made. Settlement figures can often be negotiated lower.