In a house in Kiloude City, a girl talks about Kyurem and I think she asks if I have one. What happens when I show one to her? I'm hoping she might give the DNA Splicers, but that seems very unlikely.
She gives you the DNA Splicer, which is the item you need to change the forms of Kyruem to Black Kyruem and White Kyruem.
So, you were right :P