To a very high degree of precision, a rainbow will cause specific pure frequencies to arrive at specific angles,

You surprise me Tilly. Cos that is utter bollocks.

Get the equipment: PMOSFET image sensor; an optical collimator lens system; an optical refraction grid; and a spectrum analyser. Source your light from natural sources, and apply an H2O mist between the refraction grid and the detectors. Do the experients. Measure the frequencies. Then come back and claim that you know what you are talking about.

And there is simply no pure frequency of light that is perceived as pink.

True. But under natural lighting conditions, within any human measurable period, no pure frequencies of light reach the human eye. They are always a mixture of refracted, reflected and incident light from many origins and filtered through whatever molecules exist on their paths from source to eye.

Update:Have you never seen pinks and purples in a sunset?