Thermal voltage of a BJT vs. diode voltage drop
There's no contradiction if you're using the model for what's it's intended for. 

The hybrid pi model is only useful for the dynamic gain of the transistor (and then at only one specific emitter current), not about the static biassing.

If you want a model for the static biassing, then a more useful one is to replace the input resistor with a diode, and the \$g_m V_{be}\$ current source with \$\beta I_b\$