The 3-transitive derangement graph maximal independent set conjecture

Let $G$ be a $3$-transitive permutation group of degree $n$ acting on a set $\Omega$, and let $\Gamma_G$ be its derangement graph. An independent set is a set of vertices containing no adjacent pair, and a coset of the stabilizer of a point is a left or right coset of a point stabilizer. The 3-transitive derangement graph conjecture. Every independent set $S$ of $\Gamma_G$ has size at most

$$\frac{|G|}{n}.$$

Equality is met if and only if $S$ is the coset of the stabilizer of a point. The source reports computational verification for the listed $3$-transitive groups of degrees $11,12,22,23,24$, and $16$, but presents the general assertion as a conjecture.