I just got done *attempting* to dye someone's hair a natural brown over a patchwork of long roots, strawberry blonde tips, and a very bleached undercolor. The roots and strawberry blonde parts turned a uniform brown, but the bleached out part turned... gray? with a blueish purpleish beige tone? A very strange color, at the very least.

Any ideas why this happened?

Sounds like you used a cool-toned brown which has gone ash where there was less pigment in the hair. Try using a neutral or golden brown.