Morse theory says that every Morse function $f$ (all critical points were non-degenerate and distinct critical points take distinct critical values.) $\#\min+\#\max-\#\mathrm{saddle}=\chi(M)$. So, in the case of torus (that its Euler char is $0$), the functions must have $\#\mathrm{saddle}-\#\max=2$. So if it has no max point, then the number of saddle points must be $2$. But this is against the fact that [all continuous functions on a compact domain attaint  at least a max a min][1]. So we should have at least a max point and at least 3 saddle point for torus. in the case of sphere is similar. 
$\#\min+\#\max-\#\mathrm{saddle}=\chi(\Bbb S^2)=2$ so having two global minima we must have $\#\max=\#\mathrm{saddle}\neq 0$.

  [1]: https://math.stackexchange.com/q/109548/272127