... falsely attributed to overpopulation, when they can be explained by poverty...
I don't see how you can divide between these two causes of someone dying without implying that you can never attribute any death to overpopulation.
As long as resources are distributed unequally, some people will have enough to live on. You could then say the rest are dying of poverty, never overpopulation. I guess if everyone simultaneously did at once of overpopulation, but when a group overpopulates, its members don't die of "overpopulation," they die of lack of whatever bottlenecks affect them at the time -- could be hunger, thirst, disease, etc. No doctor's chart has a checkbox for overpopulation.
In other words, poverty results from an unequal distribution of resources. If there were enough resources, even very poor people could get enough to live on. If they don't, doesn't that imply there isn't enough food?
If we could distribute all resources equally or even just more efficiently we could increase how many people the resources of the planet could sustain, but given billions of people with competing interests and rights, plus history that led to the system we have, can't we conclude we've created the most efficient system we can? If you can come up with a better system and get it implemented, why don't you? If you can't how can you conclude otherwise?
Given the system we have, I don't see how you can say people dying from lack of resources doesn't imply overpopulation, at least locally in a lot of places.
To be clear, I'm not arguing that we are overpopulated or not. I'm just trying to check the meaning of what you wrote -- in particular, could someone who said what you said ever accept overpopulation as long as some people still survived? To put it yet another way, as long as some people survived anywhere in the world, couldn't you say "While some places are overpopulated, that's only a local condition. We're not overpopulated everywhere, so we aren't overpopulated."