Does quantum reversibility require many worlds?

The source S sends a photon into the beam splitter below. There is a 50% chance that it will be detected at A and a 50% chance it will be detected at B.

S -----------\---------> A
             |
             |
             |

             v
             B

Now if we assume that physics is (generally) reversible we should be able to time-reverse this process. This would imply that if we send in a photon at A or B it should always appear back at S.

How can this happen? We know that if we send in a photon at A (or B) we would expect it to appear 50% of the time at S and 50% at C as below.

             C                                         C
             ^                                         ^
             |                                         |
             |                                         |
             |                                         |

S <----------\--------- A               S <------------\
                                                       |
                                                       |
                                                       |
                                                       B

In order that the photon always appears back at S and never at C we need a superposition of the two situations above such that the paths to S constructively interfere and the paths to C destructively interfere.

Thus it seems that in order to retain time-reversibility we need to assume a many-worlds view. As a photon is sent in at A (or B) it must be assumed that another photon is simultaneously sent in at B (or A) and both states weighted with the correct amplitude such that a photon appears with certainty back at S.

What do people think?