He said enough food and good health care. To counter his hypothesis, you would have to show examples of places with "enough" food and "good" health care, yet a still increasing birth rate.
Examples of places are - most places in the world. Even though standards in eg India and even Africa are not up to those of the West (and I'm not even sure of that any more unless you are rich), they are far higher than in 1900. As a result if which, after centuries of liitle increase, the world population has increased threefold. Even in the UK, the population increased hugely after about 1850 as a result of measures such as improved water and sewage treament, which are all part of healthcare.
you conveniently ignored the healthcare aspect altogether.
I could swear I mentioned health care in the context of Bin Laden's father. Population reduction (or the hope for it) has more to do with the availablility and acceptance of contraception and the status of women in backward societies. Some experts say it is to do with TV and films showing women a different way of life than just pumping out babies. These factors may or may not be linked to wealth. Just sending these people crates of money and medicine, or even investing in their infrastucture, will certainly not do it.