Anyone have any information about how important it is for a fuel tank
to maintain positive pressure on the inside? I mean *above*
atmospheric.

Part 23 only makes reference to tanks with bladders; these are
required to maintain a positive pressure so they won't collapse.

A C172, though, doesn't have bladders. The forward facing fuel vent
most likely *does* provide positive tank pressure, but that may not
actually be necessary in order to ensure fuel flow.