I don't really blame the UN. They set up an optional mechanism to review cases where a disabled person's rights might be infringed. The UK government signed up because, let's face it, there should be a way for those cases to be looked at.
If a case is referred to they can't just dismiss it out of hand, they have to give some sort of proper look at it.
The system wasn't set up to deal with the sort of agenda and funding that the CLC has.
As far as I have read, they have no jurisdiction to overturn the decision of UK courts, but presumably that is being looked at as a matter of urgency.
Best case scenario is that they pull out the stops this weekend, read the court judgements and accept that the best interests decision upholds Archie's rights, including any related to disability.
I suspect in future the UK courts will include specific consideration of any rights as a disabled person (just as they include reference to, and consideration of, the other rights of the person concerned). That will prevent these sorts of games from the CLC in future.