Why is the BJT in this circuit in active mode?
The emitter isn't tied straight to ground. That's why your equation for the base current is incorrect. 

The KVL loop around the base resistor is \$V_{th}-I_bR_{th}-V_{be}-I_ER_E=0\$. You can solve for the base current from there. Assume active region, for example, and use the equation \$I_b=\dfrac{I_E}{\beta+1}\$ somehow, to find out if the transistor is indeed in the active region.