I believe you are talking about the open-loop gain, but in non-inv amplifiers, there is a closed loop gain determined by Vout/Vin and it is not infinite. Therefore Vin cant be zero. I have tried looking it up and I found that only the Differential Input Voltage must be zero.
There tends to be confusion between Vin and the Diff. Input volt, where Vin is the voltage coming before the Rin Resistor. While, Diff input voltage is V+-V- which has to be equal to zero. I am not sure why it has to but I think it has -like you said- to with the open-loop gain which has to be infinite, but ill try makin sure.
Thanks for your help mate!