Seems like a missed opportunity to gain incredible trust with the kid.

"I've asked you whats in the box, and you've let me know you want to keep it private from me. I respect your privacy, but as you parent I need to know that whatever is in there isn't dangerous or inappropriate to take to places we need to go. Is there another adult you'd be willing to show whats in the box to if they promised not to tell me, and just let me know its safe for us to take wherever we go? Also if cardboard isn't enough to protect it, do you need me to get you a stronger plastic or steel box? Whatever it is, its clearly important to you, and if so, I want to protect it as much as you do. What is important to you is important to me because I love you."

If a parent showed this much care and respect for their privacy and for something they didn't understand, but was important to the child, I'd say that's a solid foundation for the kid to come to you later in life when something big is on the line: suicidal thoughts, them being assaulted, coming out as gay, etc.