No, I don't believe there was a mystery ship, but your so called reasons why Boxhall was seeing Californian by themselves are not enough.I believe that Mr. Boxhall was looking at the Californian because he was looking at a steamer, not at a star, because the sequence of the navigational lights he observed is consistent with the swinging of the Californian, because his testimony is consistent with the testimonies of some other eyewitnesses, because he was located at the Titanic’s port bow and because I see no evidence there was any mystery ship between the Titanic and the Californian. Therefore Mr. Boxhall was probably looking at the Californian.
-According to Boxhall the ship he saw appeared to be moving, first approached and then receded. Californian was stopped.
-According to Boxhall the ship he was looking at turned and showed what he took to be a stern light after he lost sight of the red before taking to the boat. According to Stone and Gibson, the steamer that was firing these rockets was on their port bow when the last rocket was seen and when it disappeared, which means Californian was showing a red light not a stern light to Titanic before Titanic sank.
-According to what 5/O Lowe wrote in his deposition, after he got all those other boats tied together:
"When I had got these boats tied together I still saw these [lights] in the same position, and shortly afterwards she seemed to alter her position and open her green. I knew a few minutes afterwards all the lights went out, and I did not see any more lights until I saw the lights of the Carpathia."
Good luck explaining that one.
And just so you know, you didn't have to be over on the port side of Titanic's bridge to see a ship off Titanic's port bow. And according to Rowe, the Morse lamp that was using was the one over on the port side of the bridge, not the starboard side. It was the socket used for firing distress signals that was over on the starboard side. As far as Boxhall's location, he too was all over the bridge that night, not just on the port side as you assume.