The output won't be always zero. How closely the output resembles what you've drawn will depend upon the frequency with which the input signal alternates from + to - and back, compared to the circuit's RC time constant.
The other individuals argued that since the ground is connected near the bottom of the resistor, the output voltage, which is in the far right corner, would always be zero.
The other individuals argued that since the ground is connected near the bottom of the resistor, the output voltage, which is in the far right corner, would always be zero.
That's not an argument, it's an unfounded assertion