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 $k$: 

$y[n] = f(x[n-k])\,.$