Okay, but something has to instruct that hard drive, and that file has to go through a gateway to an IP address. All those things can be found unless you take some serious precautions. Some ISPs will give up IP information to the RIAA on a mere request, without even a court order, because they cannot afford a lawsuit.
But those precautions are easy. Microsoft VirtualPC is free, so you can crank up a virtual machine on that external drive. Use encrypted file system (sorry XP Home users, you don't get it, but there are other free tools available) on that drive with an account with a password that includes at least one alt code character (stops easy cracks). Set your system to wipe the swap file when you shut down, or download a free system cleaning utility as previously mentioned. Then use an anonymous proxy, or for plausible deniability, do it over your wireless router, leaving it at the standard as-shipped configuration, which is open to public use.
Nothing is 100% in computer security except putting your computer through a blast furnace, and this is no exception. However, the time and expense to get through these simple, free defenses is quite prohibitive.
Slight correction: the ISP never has to worry about a lawsuit if it follows the procedures in the DMCA. But a medium-size ISP that gets 10 RIAA subpoenas a month often can't afford the lawyers to challenge them all in order to protect its clients.
I don't know if you are familiar with newsgroups. But there is a lot of stuff besides music on the usenet. And I use a premium news service. Anything is possible, but the resources required to come after me via that route make it a lot easier for RIAA to get the file sharing people.
And back to my original point, there is absolutely no evidence that I have downloaded any copyrighted music files. The usenet doesn't work that way. There is no file sharing software involved with newsgroups.