If they have gift buddies, then he should have a gift for his buddy and not for this girl. No one else is getting 2 gifts, and the purpose of gift buddies is so everyone gets exactly one gift.
If your son wants to give her something outside of school, that MIGHT be appropriate. BUT it depends on a lot of things. Friends don't buy friendship with gifts or money, as others have said. It's early to encourage too much boy/girl stuff by calling it a crush. Since the families are friends, I think I would have called the girl's parents and said, "Here's where we're at. What are your thoughts, and let's agree on an approach." The girl should not feel she has to buy a gift for your son because he bought one for her, and she might feel awkward about getting something anyway, let alone about not having something to give him.
However, the horse is out of the barn on that one because you already took him to Claire's to buy something. So you either have to give the gift or tell him you've thought about it more and changed your mind. If you can instruct him on gestures of friendship that DO NOT have a reciprocating gesture, and let him know that it's nice to express friendship in a whole variety of ways, great. But you need to tell him that sometimes people get uncomfortable receiving a gift when they are NOT reciprocating. He also needs to learn the manners involved in giving a gift, and in receiving one. Start teaching manners/etiquette now.
Part of the push-back on this is that girls are taught from a young age that boys give gifts and expect something in return, and also that there are courtship rituals. Women are vilified for accepting gifts, dinner, theater tickets and then not "putting out" for the guy. Guys think they can buy a woman's affection or sexual favors. When little kids pick up on these things, it makes their parents nervous. So while this is not what your son intended, it may be a reaction you need to anticipate.
The other problem is that you may make the others feel that there is a precedent being established - now the kids are on each other's gift exchange list. This might be more than the other family wants to get into. You have the added problem that you have a relationship with her brother (but he's not getting a gift), and his father is your husband's boss.
I guess I'd either just have him give her the gift, or discuss it with the parents. But I absolutely would not allow him to take it to the gift exchange - that is SO unfair to all the other kids. Please don't do that.