Reyes isn't a global illumination algorithm, in fact it doesn't prescribe any kind of illumination at all. Global illumination was first described by Cindy Goral, Ken Torrance and Donald Greenberg in the constrained setting of diffuse reflectance in polygonal scenes; the first general GI algorithm, path tracing, was introduced in 1986 by James Kajiya.

https://en.wikipedia.org/wiki/Radiosity_(computer_graphics)

The way I implement REYES, it does. But no doubt- Kajiya was the man.

I'm curious how you would solve the GI problem with Reyes; note that doing something like like photon mapping or radiosity isn't Reyes itself.

Photon mapping. I've never gotten radiosity debugged properly. I tend to like Reyes as something that works for NURB tersellation for me than the triangle interpolation thing. It could be that I'm a lazy programmer that has trouble with textures using classic z-buff techniques.