Yes this point is not stressed often enough: and apart from the solidarity networks you mention, I have the impression (but do correct me if I'm wrong) that three things are also missing in comparing rural to urban poverty: barter, self-sustaining agriculture and use of common resources (dead wood / water from wells and streams / hunting etc). None of these, I think register in the income or poverty estimations, so the people involved show zero income when in fact the real value of all of the above is non-negligible.

Add to this also the added value to the poor from public services - see for example the increased cost of health care after the collapse of the public system in China:

according to the government's own estimates, in less than a generation a rural population that once enjoyed universal, if rudimentary, coverage is now 79 percent uninsured.

Does this collapse register anywhere in the calculations for the evolution of poverty in China?

So we have two trends here over the past decades: urbanization as the rural populations of the world diminish and the reduction of public services. If I have understood the way GDP, income and poverty are measured, these trends would both serve to present a decline in poverty where there isn't really one.

The road of excess leads to the palace of wisdom - William Blake