If I remember rightly, the study tested whether a particular peanut
protein showed up in mom's milk after she either ate peanuts or
consumed peanut oil.  The study showed that it did show up in SOME
moms' milk, but not all.  I don't think they studied whether it
affected their babies.  The article was a while back, so I don't
guarantee that my recollection is precise.
I tell moms that most babies are fine with whatever mom eats.  If
she avoided everything that someone, somewhere says she shouldn't
eat, she'd starve!  I point out that moms in other cultures nurse
just fine even though they may traditionally eat what we might
consider strong foods.  For the most part, she should eat whatever
she wants and if baby seems to have some consistent gas, rash or
colic problems, then do a little detective work to see if she needs
to eliminate anything from her diet.  I do mention that if anyone in
either her or dad's family has a severe food reaction (e.g. it makes
them have trouble breathing), most commonly peanuts or shellfish,
then she probably should use that particular food cautiously (in
small amounts) at first until she is sure baby didn't "inherit" the
sensitivity.  I added this to my discussion after reading on Lactnet
about some babies whose family had a problem with peanuts also
seemed to have a problem.  Of course, we're talking about when the
person with the sensitivity is someone other than mom.  If it's her,
of course she should avoid the food for her own sake.
Winnie

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