Although a large body of recent work supports the formation of the He II 304 A resonance line by collisional excitation in the quiet sun, the formation mechanism is less clear in strong coronal active regions and flares. The 1989 May 5 flight of the Goddard Solar Extreme Ultraviolet Rocket Telescope and Spectrograph (SERTS-3) provided a data set that is well suited to addressing this question. This paper develops a method of assessment of the line formation mechanism that is based on simple non-LTE theory and is applied to these data. The results support the conclusion of other authors that the 304 A line is formed by collisional excitation in the quiet sun, but that photoionization-recombination (p-r) may play a significant role in coronal active regions, and that p-r is important, and may even be predominant, in many flares.