Generally, when theologians talk about the interrelationship between the true, the good, and the beautiful (and sometimes unity), they are generally talking about transcendentals. These are properties that are considered to be common to all things, which classical theologians see as finding their origins in the person of God. So when theologians talk about that which is true being beautiful, they are generally talking about that which is true to all things or all things within a category.
So a Christian might say that is true that all people regardless of race, religion, gender, sexuality, or any other characteristic are worthy of love, honour, and respect because they are made in the image of God. The theologian would say this is true, and that truth is both good and beautiful.
In the video, the narrator and the speaker, seem to want to make an argument along these classicist lines. That the “gratuitous beauty” of nature reflects what they believe is true about nature, ie. that it is created by divine intelligence.
Ironically, I agree with the premise (nature reveals God’s nature), but could not disagree more with their conclusions (therefore, evolution is hooey).
That said, I completely agree, @Kendel, from a very important perspective not all that is true or truthful, is beautiful. There is nothing beautiful about the fact (truth) that racism still exists in the world (let alone the church). So I don’t want you to think that the above is disagreeing with you. I think what you’ve actually done is highlighted a weakness in this kind of theological reasoning, highlighted the need to define terms, and shown that our understanding of what is “true” also needs to account for that which we consider evil, repugnant, and morally reprehensible.