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 not depend neither on past (for the causal case) nor future values, only the current ones, to determine the current value of the output. The output at $n$ only depends on inputs at $n$.
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 $k$:
$y[n] = f(x[n-k])\,.$