This really isn't true. My dad has spent a big %-age of his life working on family planning in the third world. It's a tremendous challenge getting people to use birth control, even in places without effective food aid.
Everything I've read says it's indeed a tremendous challenge, mainly for religious/cultural reasons. (They don't want to use birth control, and/or they want lots of kids even if they can't support them.) That's why the solution must include consequences for the parents who have children they can't support, like loss of freedom. If the consequences can't be enacted (e.g. it would take war to enact them) it may be best to do nothing and let Nature sort it out. I haven't read of family planning efforts in the third world (as aid from the first world) including such consequences.
