  We discuss the connection between the incompatibility of quantum
measurements, as captured by the notion of joint measurability, and the
violation of Bell inequalities. Specifically, we present explicitly a given a
set of non jointly measurable POVMs $\mathcal{M}_A$ with the following
property. Considering a bipartite Bell test where Alice uses $\mathcal{M}_A$,
then for any possible shared entangled state $\rho$ and any set of (possibly
infinitely many) POVMs $\mathcal{N}_B$ performed by Bob, the resulting
statistics admits a local model, and can thus never violate any Bell
inequality. This shows that quantum measurement incompatibility does not imply
Bell nonlocality in general.
