Binary Search Tree Traversal output validity and unique BST construction
I believe you are correct. The hard part is convincing yourself why this is true, I guess.

The key to the riddle is the root. preorder, postorder and levelorder all have the root at first or last position. Once the root is known all elements smaller go in the left subtree and those larger go right. Thus reconstructing the tree from its order is a recursive process.

Inorder always yields the elements from small to large, so there the situation is completely different. There is no unique tree, and any tree that is built by adding the elements as a BST will do.