To reproduce:
1) Create new project
2) Add 2 cubes to scene, make sure you can see them as two separate objects
3) Add a OnMouseDown() debug message to cubes to see when you click them, for example:

using UnityEngine;
using System.Collections;
public class Scrip : MonoBehaviour {
void OnMouseDown() {Debug.Log ("I am " + name);}
}

4) Play the scene, at first objects interact normally and clicking on empty space doesn't create any messages.
5) Change camera's Clear Flags property to "Depth Only" or "Don't Clear" and play the scene again
6) Now when clicking on empty space, the script of last triggered object triggers

Also, if there are two cameras and one of them is set to "Skybox" or "Solid color", the issue doesn't appear