I asked a lawyer this, and the rule is actually that private companies operating on behalf of the government *are* subject (this covers things like PFI contractors, franchised binmen etc.) - presumably the Law Lords decided the care home in this case was engaged in a private transaction with the lady in this case and not acting as a public body. I'm rather surprised, since there's no doubt that the state put her there and paid for her to be there (one of the arguments against is that this only covers her care, not the running of the home itself). I suspect this isn't the end of it.
The ruling is here
http://www.publications.parliament.u...620/birm-1.htm
What's notable is that it's a split decision 3-2 - Lord Bingham and Baroness Hale for, the other three against. Reading Lord Scott's judgment I think he's talking rubbish, personally - essentially he's arguing that it would be silly to treat any private bodies as executing a public function because it would be silly to treat all of them as such. Not sure I follow that, my Lord.
Note that this is an argument over a section of the HRA, not the European Convention on Human Rights, which leaves it up to the member state to decide where the state ends and the private sector begins. Their Lordships decided that since the HRA doesn't cover the care home, you can't claim that the ECHR applies. Therefore it's up to Parliament to fix it.
The Baha Moussa case is a shame on the entire country - there's no doubt that the soldiers involved killed him and covered it up for each other. Totally different kettle of fish.