Why is this current source with both sides grounded still supplying current
You're interpreting the operation of the current source wrongly. For the current source to provide a current of \$g_mV_{\pi}\$ (or any current, for that matter) into a \$0\small \:\Omega\$ load it must have \$0\$ V across it. If it were supplying a load other than \$0\small \:\Omega\$, it would have a voltage other than \$0\$ V across it. 

Your equation is wrong, btw, there are brackets missing.