Let $T$ be a discrete group, $X$ a compact metric space, and consider the flow $(X,T)$ (so that $T$ acts continuously on $X$). We say that $X$ is almost automorphic if and only if there is a point $x\in X$ with dense orbit and such that whenever $\{t_i\}\subset T$ is a net in $T$ with $\lim_{i}t_ix=y$, then also $\lim_i t_i^{-1} y$ exists and equals $x$. We define `distal' as not proximal, and we say two points $x,y\in X$ are proximal if and only if $\inf_{t\in T} d(tx,ty)=0$.
Now, somewhere, I found the claim that almost automorphic points are distal, which to me is not completely obvious, although potentially intuitive.
Can someone give me a hint on how I could go about proving this myself?
Addendum: Here, it is shown that every almost automorphic flow is a special extension of its maximal equicontinuous factor. If we let $\phi:X\rightarrow Y$ be a homomorphism of $X$ onto its mef $Y$ and if $x\in X$ is an almost automorphic point, then $\phi^{-1}(\phi(x))=x$, in other words, there is a $y\in Y$ whose preimage under $\phi$ is a singleton. This would automatically mean that $x$ is distal. However, I find the proof there rather convoluted, and was wondering if there is a simple proof of the distality of almost automorphic points from first principles, or perhaps using some elementary properties of the enveloping semigroup $E(X)$.