Since you posted that before I posted the corrected link to the Weiss article, I must presume you haven't read it yet and thus do not know what he says the various hypotheses are.
In a nutshell, one has to imagine that all of the ancestors in these phylas happened to use pretty much the same selection of resources when faced with the need to see light. That does not speak to random mutation but genetic pre-programming.
There are only so many excellent solutions to the survive and multiply movement of lifeforms. The less than excellent solutions disappear because they are eaten. It might be noted that sensitivity to light is not restricted to eye constructions. Transistors have this sensitivity, as to diazo dyes and in fact any chemical bonds.