  To simulate noisy boson sampling approximating it by only the lower-order
multi-boson interferences (e.g., by a smaller number of interfering bosons and
classical particles) is very popular idea. I show that the output data from any
such classical simulations can be efficiently distinguished from that of the
quantum device they try to simulate, even with finite noise in the latter. The
distinguishing datasets can be the experimental estimates of some large
probabilities, a wide class of such is presented. This is a sequel of
\textit{Quantum} \textbf{5}, 423 (2021), where I present more accessible
account of the main result enhanced by additional insight on the contribution
from the higher-order multi-boson interferences in presence of noise.
