You are obviously right with needing local knowledge first. But I've seen two types of well-used consulting:

1. A small team needs to integrate with an external data source. They figure out it's better to keep own engineers focused on the business logic and bring external folk for the (hopefully) one-off task of figuring out the idiosyncrasies of the thing.

2. A large company needs to push the edges. They hire someone with a PhD in the general area, who then points at the exact professors needed on board to get the edges pushed.