The point is, there might be a mismatch between our model and the underlying reality. There could be an unknown deeper structure to reality which explained why those values appear to us as “fine tuned”.
I'm not assuming the constants can be changed; axiomatically, they cannot, because they're fundamental constants of the universe. I'm also not assuming that some agent was around to do the tuning. In its basic form 'fine tuning' just means that if one of the values were even slightly different we wouldn't have anything like the universe we see today, including life. The values of the constants appear as if they were tuned.
It's interesting you bring up evolution, because before that theory came about intelligent design was a reasonable assumption in trying to explain how well-adapted organisms seemed to be to their environments. It was as if someone had designed them for their roles! As it turns out the theory of evolution satisfactorily explains why organisms exhibit the appearance of design.
In a similar way the fundamental constants exhibit the appearance of having been precisely set. It's hard to imagine a scientific theory getting 'behind' the constants the way evolution was able to get 'behind' the appearance of organisms...
This is a hallmark of a chaotic system. It's not impossible but the chances of sitting exactly on such an unstable point seems very low. It seems more likely that the constants are some optimum in a basin of attraction, a stable point in some higher order dynamic system.
They're constants but are they fundamental? There are a lot (19?) of free parameters in the Standard Model. We determine them experimentally. But that doesn't mean that there isn't some deeper explanation that results in those values. We just don't know what it is yet.
That said, I believe the chain of logic (haven't watched the PBS video yet) is simply that were these fine-tuned constants to take any other value, there wouldn't be intelligent life to observe them. If the values were to be anything outside a narrow range, they would remain unobservable by entities within that hypothetical universe, and because we are making an observation we are implicitly sampling from the distribution of observable values. It's a Bayesian metaphysical argument?
That sounds like it presumes a multiverse, but I don't think you need an infinite number of universes or a god for that to be true... that said, it does purport to explain how fine-tuning doesn't violate certain (metaphysical?) principles of science that call for "naturalness" (which a friend once told me boils down to "all unitless constants should be either 1 or 0 otherwise it's inelegant" or something): the fine structure constant is what it is because otherwise nothing would exist to observe that it was 1/139 or 42 or whatever.
I hope this is even slightly more satisfying to read than it was to write.
Nothing says that they couldn't be changed, but then there's the question of _why_ they can't be changed. What forced them to be the values they are? Some of them appear to be free, so are they?
We could just as easily say that life on earth was “tuned” to make ”intelligent life” evolve, but we don’t have any other 4 billion year test runs of earth to see what else might have evolved. In the same way we have no data at all about the phase space of other possible universes, their constants, or how their physics would play out on cosmological timescales.
It’s not that it isn’t fun to think about. It’s just that it is unscientific.