No, it is an opinion. Tazawa and Uehara, and to a lesser extent Miller, have been incredibly reliable relief pitchers and in all likelihood would be able to make the transition from the 8th to the 9th inning without too much effort.
Your "fact" is that the Sox have no reliable closer, which cannot be true because you have never seen Tazawa or Uehara as a closer and so cannot judge their reliability. All you can judge is their reliability as relief pitchers in general, which has been above reproach.
Your second "fact" is that the Sox have no proven closer, which is patently untrue. They have two. Hanrahan, who is on the DL, and Bailey, who is currently the closer and has proven himself as one for a few seasons now. The fact that he has struggled recently does not make him an unproven closer, it just makes him a proven closer who is struggling.
My opinion is that Bailey has hit a rough stretch. He may pull out of it, or he may spiral and be taken out of the closer's spot, designated for assignment, and in a year or two could be selling cars and living in a studio apartment that he shares with Manny Delcarmen and Daniel Bard. If he doesn't find himself again, my opinion is that Tazawa, Uehara, or Miller could take over the closing role without imploding like an egg on the bottom of the ocean.