  Recently, Glasner, Tsankov, Weiss, and Zucker showed that if $\Gamma$ is an
infinite discrete group, then every minimal $\Gamma$-flow is disjoint from the
Bernoulli shift $2^\Gamma$. Their proof is somewhat involved; in particular, it
invokes separate arguments for different classes of groups. In this note, we
give a short and self-contained proof of their result using purely
combinatorial methods applicable to all groups at once. Our proof relies on the
Lov\'{a}sz Local Lemma, an important tool in probabilistic combinatorics that
has recently found several applications in the study of dynamical systems.
