Return of inner class instance works in header but not in definition cpp file

I have a .cpp file which defines the header file.

#pragma once

/*
    Properties of Binary Search Tree:

    1.) Elements less than root will go to the left child of root
    2.) Elements greater than root will go to the right child of root
*/

#include <memory>

// Binary Search Tree handler class
class BSTHeader {

    /*
        Naive implementation of BSTNode (non-generic version)

        Nested class is private, but it's internal fields and member functions 
        are public to outer class: BSTHeader
    */
    class BSTNode {
    public:
        int data;
        std::unique_ptr<BSTNode> left;
        std::unique_ptr<BSTNode> right;

        BSTNode(int val) {
            data = val;
            left = nullptr;
            right = nullptr;
        }
        ~BSTNode() {}
    };

    // Internal fields
    std::unique_ptr<BSTNode> root;           // Root of BST
    unsigned int size;                       // Total amount of nodes in tree from root

    // Internal methods
    bool insert(std::unique_ptr<BSTNode>& root, int val);
    bool search(std::unique_ptr<BSTNode>& root, int val);
    std::unique_ptr<BSTNode>& find_min(std::unique_ptr<BSTNode>& root) {
        if (root.get()->left == nullptr) {
            return root;
        }
        else {
            return find_min(root.get()->left);
        }
    }

public:
    BSTHeader();
    BSTHeader(int val);
    ~BSTHeader();

    // API
    bool insert(int val);
    bool search(int val);
    // Getters
    int get_root_val();
}

The nested class BSTNode is private. However when I try to declare a function std::unique_ptr<BSTNode> find_min(std::unique_ptr<BSTNode>& root) in the header and define it in the .cpp file, I get an access error since I cannot return a smart pointer to a private object (makes sense, but this is a private function and i'm only defining it!). But I do not get an error if I define the function within the header file like I have above.

Is there a reason why it returns an error in the .cpp file defining the function but not when it is defined in the header file even though it is a private method? Do I have to declare and define all methods in the header file that returns a smart pointer to a BSTNode?