From the sound of it, I likely(?) agree with the hosts on this, but I think I might look at it a different way. Or "splitting hairs".
There's a difference between "taking away agency" and "entering a restrictive situation". Just because you're captured doesn't mean you don't have agency or that it's been "take away" from you. Player agency is simply the freedom to have your character take any action your character is able to do in the present situation.
If you're KO'd, mind-controlled, dead, etc - sure, you might not be able to do anything, but neither can your character. The GM isn't "taking away" agency - something happened in the fiction as a result of unfolding events that resulted in a restriction on what your character is able to do. In my opinion, thinking about this as if someone is "taking something away" from you seems an unnecessarily adversarial position. (which is really the crux of the reason for this post)
Sometimes restrictive situations are less fun - and the GM should definitely be mindful of that (see: Chad's "payback with interest") - but the simple occurrence of those situations don't indicate the GM is doing anything incorrectly or arbitrarily "taking something away" from the player. Like Wayne said early on, if you avoid all this entirely, you really can't have any "consequences" in the game - and I don't even mean "consequences" in a punitive sense.
Something ALWAYS restricts what your character can do. Everything from gravity, to the city watch, to your character's stats and abilities restrict what you can do. As you've mentioned several times, the favorite lie of RPGs is "you can do anything".
To me, it's only "taking away agency" if the GM just arbitrarily says a character can't do something - or that something happens to this character - by fiat (circumventing mechanics/"fairness") and without regard to player input.
Starting a game in a restrictive situation (captured, etc) isn't really "taking away agency" either - it's setting up the story. The story has to start somewhere, and at some point on the "restricted options" continuum. It may or may not be a good idea, but that's kind of a different thing.
You can, of course, debate the finer points here - i.e., is it "taking away agency" if the GM sets the DC for the save-or-suck to an impossible number? Yeah, probably. What if the GM repeatedly puts the characters into situations where their options are severely limited? That's basically a railroad. Is it "taking away agency" if the GM ambushes you and says you're captured without giving you the chance to fight back or avoid it? Yes - because you as a player were prevented from doing something the narrative and mechanics suggest you should be able to. "Taking away agency" or not, there are any number dick moves GMs can make. They shouldn't do that stuff.
"One Penguin to Rule Them All..."