As far as clipping in, I'd say "whatever works for you," with the exception of climbing steep hills, where you do pull up quite a bit on the upstroke, and where your foot slipping off the pedal is extra likely because of the forces involved, yet could be disastrous.

But as far as the benefit of stiff soles, that article is way off base. Rhumpty-mumble years ago, when I got my first pair of cycling shoes, it added 1.5 mph (about 8%) to my average speed over a particular course, doing nothing else different - and that was a flat course. A pure 8% efficiency gain, just from the shoes. Your feet can't support themselves cycling as they do walking for the simple reason that your pedal is not the size of your whole foot. When walking or running, your points of attachment to the ground are the two corners of your heel, the heads of your first and fifth metatarsals, and your big toe. There's no bicycle pedal in the world that big, and there are reasons for that. (I'll leave the barefoot/foot pathology discussion to the running subforum, there's plenty of it there).