Your example is quite interesting.
With a constant output, it's hard to distinguish which input it is responding to. You can say it's y(t)=x(t) or y(t)=x(t-1) or y(t)=x(t+1).
Yet for such a system, no previous or future states are needed to remember as they yield the same output. So take it as a whole I agree that it would be memoryless.
Regards,
Xujun Huang
