Is this true for very wealthy people, or only for above average earners?
There are many examples of very wealthy people having lots of children. Children are still a significant investment for high earners, but at a certain wealth level it becomes inconsequential.
Quick google shows some support for this idea:
"There is a new emerging trend where better-off men and women are more likely to have children than less well-off men and women."
ergo, there is probably a level of financial support/wealth at which people start having more children. Or more simply, the point at which the personal benefits outweigh the personal costs.