Propellant tank pressurization is a critical aspect of liquid propellant rocket design. Many designs use high pressure helium, heated and recirculated, however the propellant gases themselves can be used - at least in the case of LH2 as explained in this answer. In the case of Falcon 9 this is mentioned here and here as I've learned in the discussion and links associated with this question.
Another question Why do pressure-fed systems have to be pressurized with helium or nitrogen? addresses the question of why the choice of pressurization gas must be helium or nitrogen, and self-pressurized by their own boil-off gas. This is a different question. I am asking about the function or purpose of the pressurization, and the relative importance of two following possibilities.
I had thought the pressure was necessary only to feed the propellants into the pumps and other plumbing of the engine fast enough, but then I saw this line in the CSMonitor article: SpaceX launch explosion traced to helium system. Now what?:
Helium is injected into fuel tanks to keep them structurally sound as the launcher burns fuel during flight. This system apparently leaked during the static test.
Thinking about it, overpressure would certainly help maintain rigidity of the tank. Anyone who's seen the "crush the can" experiment can't forget it.
Question: Is the pressurization of propellant tanks actually necessary for structural integrity? And while maintaining pressure above ambient may be necessary to prevent buckling, is further positive pressure used in the mechanical design of a rocket to substantially stiffen the structure?
above: Image of the "Crush the Can" experiment, Ronald Lane Reese, Johns Hopkins University (1999).