That is about something entirely different. It more or less just says that energy might be lost if you have a flux towards infinity. It does not in any way clai

That is about something entirely different. It more or less just says that energy might be lost if you have a flux towards infinity. It does not in any way claim e.g. that the divergence of the stress energy tensor is non-zero (which would be how I think most people would interpret energy/momentum conservation).