I don't see anything wrong with wearing black or brown shoes with navy or grey. I used to agree w/the OP that brown and grey were from 2 different color families, ergo don't wear 'em together. But by that token, blue suits shouldn't go with brown OR black - so where would that leave you?
A woman running a tasting room in Monterey once gave me the best advice on wine: If it tastes good to you, it's a good wine. I tend to err in that direction with sartorial choices.
seems to me grey suit.... brown shoes. I fought it at first, thinking why fight a color story? Turns out a slight contrast is achievable while staying conservative. A black shoe is safe and a good standby but inside the box. A good oxblood, always a favorite, goes with any suit already owned. Damn me for it. Layer upon layer, colour, within a season appropriate texture is always well received. A grey suit is always and will continue to be a favorite, pin stripped, chalk stripped and window pain. Doesn't matter. It continues to be a blank canvas with nothing but color options available.
on the debate goes, which shade of navy? And how to classify them. So a darker navy considered a classic. dark brown shoe no question. This rule travels with new navy or spring navy, lighter shade of brown shoe fallowing the colour story.