Extra element theorem
I'm not familiar with EET, but this is my interpretation of the problem. You can ignore the entirety of the circuit and focus only on the output voltage (here \$V_o\$) with added \$V_1\$:



simulate this circuit &ndash; Schematic created using CircuitLab
Without the &quot;distractions&quot; from the rest of the circuit, you can note the additional source \$V_1\$ causes the relation \$V_o=V_1\$. You state your goal as &quot;solve for \$Z_{out,0}=V_1/I_1\$, such that \$V_o\$ is zero&quot;. Well, if we enforce the constraint \$V_o=0\$ in this circuit, it must follow \$V_1=0\$, therefore \$Z_{out,0}=0\$.
The solution mention to &quot;infinite current&quot; arises if we were to try and force \$V_1\neq0\$. In this situation, regardless, it still follows that \$V_o=V_1\$ so therefore \$Z_{out,0}=0\$, and the only way one can get a zero ratio from a nonzero numerator (\$V_1\$), is to have an infinite denominator (\$I_1\$). This seems to be an obtuse attempt at a proof by contradiction, being the original proposition \$V_1=0\$ assumed to be false.