I think GP's point is that one vulnerable hardware or software implementation in the entire network of implementations being passively observed by the attacker can reveal the private keys. So it's not just your implementations which must be perfect, but all your neighbors, and all theirs too.
I read it as "only" the signing machine needs faulty hardware. Still, bit errors occur, even with ECC, and this allows for a passive hence very unobtrusive attack.
My point was exactly that, it's bloody hard. Not only implementing it correctly, but all the non-obvious ways it can go wrong that'spartially out of your control due to non-ideal hardware (in the mathematical sense). Timing attacks, cache leaks, speculation leaks, this...
