Also, the apse isn't facing due south. You can tell from the compass rose on the diagram from the Israeli Antiquities Agency (here) that it's a little east of south, about 175°. The compass heading from there to Mecca is 154°.
That's a 19° difference. Archaeologists state the Muhammadans were unusually precise (for the period) with the orientation of the apses, 50% being within 3° of the compass heading to Mecca and 80% within 5°. So either this was an outlier or it was never intended to be pointing toward Mecca.
In his documentary, Islam: The Untold Story, author Tom Holland is shown to the ruins of an early mosque (+/- 100 years after Muhammad's death) in Israel by Antiquities Authority archaeologist Dr. Tali Erickson-Gini (about 40 minutes into the video). That particular mosque has its apse facing to the east, which she remarks was not uncommon among early mosques, giving her to speculate that they simply might not have yet decided which direction they were supposed to be praying in.
There is no surviving evidence linking the desert sanctuary mentioned in the Quran with the city of Mecca until more than a century after Muhammad's death. Holland speculates that the location of Mecca was chosen out of political expediency by early 8th century Arab leaders who were intent on co-opting Islam to use as a social control over the masses. He offers that Mecca in particular might have been chosen because at that time it was free from any contamination from Jews or Christians.
In any case the Muhammadans have nothing but camp fire stories to support their claim that Mecca was this desert sanctuary.