... don't they? (in the long run)

In the "long-long run", given ad hoc reproductive patterns, yeah, I'd expect evolution to ratchet average human fertility higher & higher until much of humanity slammed into the Malthusian limit, at which point "when people have more food they have more kids" would become true.

Nonetheless, it isn't true today, it's unlikely to be true for the next few centuries unless WWIII kicks off, and may never come to pass (humanity might snuff itself out of existence before we go Malthusian, or the threat of Malthusian Assured Destruction might compel humanity to enforce involuntary fertility limits). So here in 2014 I rate the idea incontrovertibly false.