  The concept of explainability is envisioned to satisfy society's demands for
transparency on machine learning decisions. The concept is simple: like humans,
algorithms should explain the rationale behind their decisions so that their
fairness can be assessed. While this approach is promising in a local context
(e.g. to explain a model during debugging at training time), we argue that this
reasoning cannot simply be transposed in a remote context, where a trained
model by a service provider is only accessible through its API. This is
problematic as it constitutes precisely the target use-case requiring
transparency from a societal perspective. Through an analogy with a club
bouncer (which may provide untruthful explanations upon customer reject), we
show that providing explanations cannot prevent a remote service from lying
about the true reasons leading to its decisions. More precisely, we prove the
impossibility of remote explainability for single explanations, by constructing
an attack on explanations that hides discriminatory features to the querying
user. We provide an example implementation of this attack. We then show that
the probability that an observer spots the attack, using several explanations
for attempting to find incoherences, is low in practical settings. This
undermines the very concept of remote explainability in general.
