The BBC have found a form of words they can use to describe the importance to Judaism of the Western Wall that they hope will stop them receiving complaints about misleading people and more importantly prevent them having to acknowledge that there's a mosque built on top of Judaism's holiest site.
This BBC report http://www.bbc.co.uk/news/world-us-canada-40003636 is the first that I have noticed using the wording 'Judaism's holiest prayer site' to describe the Western (or Wailing) Wall.
The Western Wall is indeed the holiest site that Jews can pray at but that's because there's a mosque built on top of Judaism's holiest site. That site being out of bounds for Jews to pray at. A restriction that is enforced by the Jewish State of Israel, in contrast with the way that Jordan banned Jews from even the Western Wall when they were in occupation of Jerusalem between 1948 and 1967.