former

The index that you are measuring correlation with is the local market index in the case of segmented markets (the “global” portfolio is really just the local market portfolio). The reason the correlation is 1 is because there is no impact from other markets, as it is fully segmented.
It doesn’t explicitly state it for the integrated markets, but i would have to think the global portfolio is actually a true global portfolio, when you calculate integrated market equity risk premia.
I think you are comparing two different benchmarks, local market for segmented, global market for integrated.