Those wealth statistics really are dodgy. Another edge case: you're earning so little that you don't save, but spend it all on food/housing/etc. Now your country's economy takes off and you suddenly earn 20% more. You're still spending it all, enjoying much better and healthier food. To those statistics, nothing changed.

Net income is a much better metric than wealth.

One edge case? Look at the debt levels in the US! There is a huge chunk of the population that has a negative net worth, mostly due to mortgage debt.

Is it fair to say all those people are poorer than people in India who have a few dollars to their name?

Well, show me a perfect metric that doesn't have similar edge cases?

For example, income has its own issues -- a retiree can have little income but a big retirement fund to draw down.

In an ideal world, you'd probably measure something like current net wealth + discounted expected future earnings, and maybe use PPP instead of GDP, except now you're trying to measure two things accurately instead of one, and making guesses about the future too.