There isn't a basis. Marc Okrand created several "just because" things in the language. This is one of them. Specifically, he wanted to avoid any verb meaning to be, because he thought that would be fun, but not for any deeper reason. So he came up with a way to shove nouns and pronouns together that can be used in the same places that other languages use to be. But it's just a more or less arbitrary formula to follow. There's nothing to grok here.
I'm not confident of that. And I totally understand what you're saying.
But a Klingon does understand Being. Or else he would not be self-aware. The Klingon language developed in different ways than ours. He does not follow an arbitrary set of rules when he expresses that, "He is."
Don't forget, a Professor made this up. My guess is that it Does make sense in some real (alien) way.
You can understand a concept without having a word for it in your language. Klingons don't need a word for be because they other tools to accomplish the same thing. You're confusing philosophy with linguistics.
I've spoken with Marc Okrand many times, as have most (maybe all) of the creators/moderators of this course. We've all asked him about how he came up with Klingon, and he's given lectures on the topic. A big topic is always that there is no "to be" in Klingon. It's because he just wanted Klingon to be "difficult" in that way. There was no master plan or deep insight. Pseudo-quote: "All languages have a verb to be, so Klingon doesn't."
Here's a clip of him explaining how he didn't know much about making constructed languages when he made Klingon, and why he did what he did: https://youtu.be/9YnYTSy0iYs?t=3m