By only allowing people who don't know anything secret to work on a product, you keep the product safe from allegations (justified or not) of illegally incorporating third party material.
If you don't do it, you risk that a competitor claims "your product contains our proprietary material, pay us royalties or we'll sue your customers". Even if you're 100% in the right, until you've had that decided in court, your customers have to worry about getting sued, and you'll lose business (and also spend a lot of money on lawyers).
The model is particularly known/used in reverse engineering: One team (that is not tainted with knowing any NDA'd materials, I assume) looks at the product you're trying to reverse engineer, and writes a specification. Another team (not tainted by NDA'd knowledge or knowldege of the code of the original product) then implements the spec. https://en.wikipedia.org/wiki/Clean_room_design
How about security secrets which directly impacts the customer?