That's backwards. Not "anyone" can program computers. Anyone can try, but most will fail. Just like "anyone" can "do math" or "do chemistry" or "do anything", but most will fail. The reason programming is lucrative, whether as an employee or entrepeneur exploiting programmers' labor (or supplying their own technical labor), is exactly because not everybody can program well enough to meet a market need.
It's a curious thing, this misplaced, or in some cases faux-humility about programming, or any other academic/intellectual endeavour. It dovetails very well with certain business interests who would love for nothing more than programming to be as commoditized as, say, janitorial work is. These interests are definitely getting their wish in some areas (e.g. web/mobile development).