You know, I'm wondering if some of these occurances in birds could possibly be bilateral gynadromorphism, where one chromosome gets lost, and the organism ends up having both male and female traits. It's more likely to happen with gender dimorphic birds like cardinals, chickens, or eclectus parrots, but I was thinking more on the lines of inherited sex-based mutations. Granted, I have no idea how budgie color mutations work, and I'm still trying to figure it out with cockatiels.
I have a bit of a better idea of it though.
But just to throw a crazy and unlikely situation as an example out there, let's say Shodu and Buster lay a clutch, and to the whole community's confusion and excitement, one of the babies is a half-sider, with one half being grey, and one half being cinnamon. Because Cinnamon is one of the sex-linked recessive traits, and only found visible in their female chicks, and the grey chicks are males (with the possibility of an exception, according to Carolyn
Still waiting to see that actually happen), would that make the chick a gynadromorph?
Here's an example of what gynadromorphism looks like in birds. Grey cardinals are female while red ones are male.