It actually has more to do with your and BD;s allergies then anything. They say that if you're allergic to a lot of things or your significant other is, especially if he is to peanuts, then you shouldnt eat em while pregnant or breast feeding. IF you guys dont have allergies and such (food allergies) then you'll be fine more then likely.
Usually it's an allergy to the protein, and the proteins would be spread through breastfeeding... So it could be possible. My friends son got hives anytime his mom ate peanuts. This would be the same for any allergy, though.. not just peanuts. Peanuts just so happen to be the most common. My daughter has issues with dairy, and can't tolerate it through breastfeeding and absolutely refuses to eat/drink anything dairy.
Also, my son never had a peanut reaction while breastfeeding and it never showed up until he was introduced to peanuts themselves. My daughter, as far as I can tell, is not alleric.