They sure can't win in court as they're not informed that they're being judged before the judgment is passed. There is no possible defense.
> on something as difficult to prove as "neglecting to secure your internet access"
If the Hadopi said they caught your IP, the evidence is given. They don't have to prove you neglected to secure your access, it's you who shall prove you didn't neglect it by installing a government-approved spyware on your Windows-only PC.
Personally, at the first warning I will get a VPN. The defense is simple.