Is the switch representation for this logic wrong?
The switches are correct. The circuit will only be closed when the left switch is at \$\overline{A}\,(A=0)\$ and the right switch is at \$B\,(B=1)\$ or when the left switch is at \$A\,(A=1)\$ and the right switch is at \$\overline{B}\, (B=0)\$, thus \$\overline{A}B + A\overline{B}\$. The configuration in the drawing is showing \$A=0, B=0\$.