The way I understood it is that it's in the perspective of international investors. Therefore when the dollar is weak, they probably would find it interesting to invest in EM local debt. Would also be easier for EM companies that have dollar liabilities to repay it. But correct me if I'm wrong :)
Marianne is right. Taking external debt from the point of a EM government is cooll when the dollar is weak. If I am an investor and the dollar is weak and prefer to invest in Em local debt as in the future I get my money in Local currency and as I suppose the Em grows it should be a good deal. Furthermore, the advantage form Local debt is it is more secure as in the worst case the Em government can print money to pay me.