I don't think that's what he's saying. What Goldston et al. have proved is that Zhang's approach can't prove a bound any better than H=16 without major modifica

I don't think that's what he's saying. What Goldston et al. have proved is that Zhang's approach can't prove a bound any better than H=16 without major modifications, but it doesn't actually establish the H=16 bound. In principle, if the twin prime conjecture were only true for, say, H=20, that would still be consistent with both results.