Obwohl is very similar to although in English and there are no unexpected requirements to using it. Hence your example sentence is fine:
Obwohl die Bevölkerung in den armen Ländern stärker wächst, steigt der Wasserverbrauch besonders in den reichen Ländern.
The usage of obwohl here reflects that the reality is contrary to the expectation, namely that water consumption primarily follow population increase.
When reading this sentence, the stress should be on reichen. I think the fellow's confusion stems from unjustifiedly rendering your sentence as this implausible sentence:
Obwohl die Bevölkerung in den armen Ländern stärker wächst, steigt der Wasserverbrauch - besonders in den reichen Ländern.
Although such a deliberate addition of punctuation is not justified and he should have admitted his mistake, in the very least on second glance, this can be prevented in many ways, either replacing words, as one answer suggested, or moving besonders:
Obwohl die Bevölkerung in den armen Ländern stärker wächst, steigt der Wasserverbrauch in den reichen Ländern besonders.
Your second sentence with obwohl is equally fine. There is absolutely no reason to prefer während. The latter does nothing but introduce some ambiguity, as to whether you want to express temporal or logical relationships.
Per the request of the original poster, I now go on a detour to explain what's wrong with the dashed sentence. Most people may want to skip this to avoid being confused.
Essentially, the dash severes the link between den armen and den reichen. It is now no more possible to tell, what stärker compared. It could be anything, especially a point in time. The basic claim now becomes:
Obwohl die Bevölkerung in den armen Ländern wächst, steigt der Wasserverbrauch.
That, in turn, means that the speaker assumes a model of water consumption in which it it drops when population increases. That is not illogical in the mathematical sense, but implausible, if said without further clarification.
We can of course construct pathological models in which such a thing happens. Let's say, the desert kingdoms of Insania have but a few inhabitants. Most of them live on a cup of water per day, but the crazy Sheik wastes water in his gardens. From time to time inexplicable population explosion multiplies the number of his subjects, who rebel and in a bloody struggle force him to stop wasting water. A native of Insania might indeed exclaim:
Obwohl die Bevölkerung in den armen Ländern stärker wächst als in Insania, steigt der Wasserverbrauch.
But even in this insane scenario, the part after the dash would not fit in. To allow for that we must construct an even more surreal model: Insania is in fact a federation of states. The rich states Koeteria, Perversia and Takeallia waste water, while the poor states suffer. Every once in a while, inexplicably, the population of the poor rises so much, that they can force the rich states to spend less water.
Now the native of Insania has learned that population increase in the poor states means reduction in wasting water and in fact reduction in overall water consumption!
Thusly conditioned he may now exclaim:
Obwohl die Bevölkerung in den armen Ländern stärker wächst denn je zuvor, steigt der Wasserverbrauch - besonders in den reichen Ländern. ,
warning his fellow citizens about the imminent rebellion!