A confusion may arise, for causal systems, from mistaking "having negative signal values (amplitudes)" and "depending on negative time indices".
A strict memory-less system does depend neither on past (for the causal case) nor on future values, only the current ones, to determine the current value of the output. The output at $n$ only depends on inputs at $n$. For a strict memory-less and causal system, you could not depend on former (negative, in a way relative to the current index) time indices.
By extension, some allow memory-less systems to allow a constant delay, i.e. to hold only one value at a given lag: the output at $n$ only depends on inputs at $n-k$ of a fixed integer $k$: So, globally, memory-less system can afford the following shape, with $k$ any integer:
$$y[n] = f(x[n-k])\,.$$
For realizable causal systems, that cannot look ahead in the future, on:y $k\ge 0 $ are allowed.