Of course to start, I am not familiar with UK law. I can only presume it has its essence as the same as Copyright law in the US.
(for new people seeing the thread).
I work for an internet provider, not as large as say AOL but we do have a few hundred thousand subscribers with services ranging from fiber to
wireless, DSL and dialup etc.. Some important points I would like to say first.
I have never seen a DMCA complaint fo any farther than a cease and decist letter. All the copyright holder has is an IP address nabbed usually from a
honeypot setup though some movie encoders will rip information about the computer and embed in the video files. I can only give advice based on the
technical side related to ISPs.
If you were one of my end users. I would actually advise: Say nothing.
When we get a C&D letter we contact the end users to say "hey, some scary people are stomping their feet, might want to watch this show on hulu or
something instead of downloading.". We are not required to. in fact we could hypothetically charge the lawyers to even contact you without giving
them any input at all.
So, if we don't have to, why do we contact?
I cannot speak for any other service provider but the reason I call people is to save them a possible lawsuit. If my calling someone and telling them
about their kid downloading an ISO of a video game saves them a few thousand dollars in fees, seems worth it for a 10 minute phone call. And frankly
if you were to get mouthy with me I might just kill your account to save my company the pain of a potential supeona in the future.
As for the letter. If you were to send it to them you are telling them you are the person who was accused, signed or not. You just gave them more
informaiton than they had. I as a company can fight them because we have an in house lawyer and will force them to jump through hoops to get your
information. The same information you just willingly gave them by sending the letter.
Some aspects about the letter iteself I wanted to point out were a bit off in my oppinion.
"You assert in your letter that the infringement was apparently traced to our internet connection. We note that we are not personally being accused
of the infringement, as you have no evidence to this effect."
and
"As you seem to be perfectly aware, it is impossible to link an IP address to a particular person or computer without further detailed analysis,
which requires a level of expertise we do not possess. Furthermore the delay in your sending of a letter of claim precludes any such analysis. In your
letter you state that “it is unlikely that a simple denial (without further explanation) will change our view of the circumstances”, unfortunately
we do not have the expertise to provide a detailed explanation. As such we can only conclude that we have been a victim of foul play."
I have evidence a plenty. Either you are a DHCP customer or a static customer. When you connect your MAC address is also linked in logs. So we have
IP, usernames, mac or if a DSL customer something called a PVC (permanent virtual circuit) the PVC only goes to you. Or more specifically your
gear.
So in this paragraph I can prove your line was involved. Whether you or your neighbor etc. doesn't matter. You are the person responsible for your
internet connection. In these situations I can reasonably prove it was in fact your internet connection. You can argue someone else did it, fine. Not
my concern as an ISP though. Protect yourself. Read up on firewalls. Protect yourself.
In my opinion the email could pose more risk as it basically tells the lawyer "Bring it!" while giving them some additional ammo. Again though I am
not familiar with the laws in the UK.

