It's not true. I'm sure you knew that already
but I know it's helpful to find out you're not the only one who knows it.
Probably what happened is she met a few families with dairy-intolerant babies, and drew her own conclusions, and she's trying to "save you the trouble." I had a nurse like that, who'd seen a boy with a paraphimosis, and had declared herself the savior of all the office's baby boys-- she told me "well, the docs here will tell you you don't HAVE to circumcise him, but let me tell you I think it's crazy because here's what happens-- we see it ALL THE TIME."
(I told the doc about it, and SHE was horrified, and told me she'd "take care of it." Which I hope means they made this nurse stop telling people that stuff.)
I've been told some amazingly uninformed things by pediatrician-office nurses, over the years. A lot of them know less than the docs do, about breastfeeding, especially if they've never done it themselves. I remember patiently explaining to one nurse, when my twins were infants, about the how supply and demand works, and what letdown is. She had no idea. And she'd just got done explaining to me why I HAD to wait three hours between feeds, because if I didn't, there wouldn't be any time for me to fill up with milk again.
For the sake of information (not for the OP, specifically)-- some infants are allergic to or intolerant to casein, the protein in cow's milk and cow's milk products. The usual way this shows up is with intestinal symptoms-- signs of injury to the intestine, including mucus or blood in the stool-- and with pain or fussiness. There may also be allergic symptoms like runny nose, wheezing, or runny eyes, or skin symptoms like eczema. Many other mamas also have reported that their babies are fussy after they eat dairy products, even though there are no intestinal symptoms, and that this fussiness clears up when dairy is removed from the diet. Finally, it's important to realize that this intolerance is NOT lactose-intolerance. Lactose intolerance in adult humans is extremely common-- the norm, really. But in human infants, it is rare. Breastmilk itself contains more lactose than cow's milk, and whether mama is eating lactose herself does not change that. The allergy or intolerance is to the protein, not to the lactose, which is the sugar in milk.
I mean, he spits up quite a bit, but that's normal, right, for a 2 week old? (You'd think I'd remember from DD, but here I am wondering all over again.) 
