The PBA didn't endorse Wilhelm nor did they endorse Obama.
Police Commissioner William Bratton can be excused for trying to defend his Mayor. Even a lowly prostitute must please the source of her income. However, his statement on Face the Nation shows that he is either out of touch with reality or he was trying to deceive the public. In response to the question about the appropriateness of the officers turning their back on the mayor he stated, At the same time it is reflective of the feeling of some of our officers at this juncture. Some? The photograph of the officers showed that the entire assembly had turned their backs. Perhaps some of the officers outside of camera range did not turn their backs. Clearly the mayor has lost the support of more than some of the officers.
I don’t know what the “PBA” is but there are plenty of pictures of Obama surrounded by NYPD officers during elections. And they look real friendly.