Question about the MOSFET saturation condition
The first sentence you quoted from the solution manual has a typo. It should say,


  First of all, if \$V_{in}\le V_T\$ then \$V_{MID}=V_S\$, so the second FET ...


That is, in this condition, the "\$V_{in}\$" for the second FET is \$V_S\$.