Disagree here - this isn't a take out, since the results are still in the realm of player choice. You can take a severe broken leg (as you mentioned later) and keep fighting (or concede on your turn before the troll can hit you again), or you can negotiate for some other result of similar overall value to having taken a severe; were I a GM, I might offer an alternative of "You're pinned under a rock, and pick up a moderate consequence of bruised ribs - you're out of this fight, and getting you un-pinned will take a significant amount of effort from your allies." Killing a PC in this instance, however, is completely inappropriate.
If you can't, or, choose not to absorb the stress, it's a take-out. I'm saying,
if he doesn't take a consequence, he's taken out. You (the gm)may choose to narrate the take out as you've just said(getting pinned under a rock), but What's inappropriate about killing a PC? If it's appropriate to the situation, it happens. Maybe the scenario was a set-up and the troll was hired to kill the PC's. It was an example I made out of my head while I was typing so you can't really say what's appropriate or inappropriate. I was just illustrating the possible severity of letting an enemy choose your fate.
That's how Take Outs happen. As a GM I wouldn't kill a character like that but if you're fighting something like a Wendigo that wants to eat you, and your players are waffling between taking a severe or just getting taken out, I'd mention, "you know, that Monster wants to kill you and have you for dinner. You may want to take the severe and then concede instead of letting it decide your fate."
If the player takes out the troll, he can choose to kill the troll or have it incapacitated because the player is in charge of the narrative.
Another good option for a concession here would be something like "You dodge, trip, and find a fairly deep hole in the ground the hard way. You're a bit battered by the fall - minor consequence of "bruised and battered" - and it sounds like there's something else breathing down here... Figure out what you want to do; I'll get back to you once I'm done running the scene with the ogre and the wizard."
And this is the concession. Which you can barter if you choose to take the severe. But not if you choose to let the troll Take you Out.
There's one part of this that's just wrong: the player does still get the fate point for accepting. Doesn't matter that it was a free tag - that only triggers the compel. Much like if another PC were to try and compel an aspect on your sheet - they only trigger the compel; the GM handles it from there like any other compel.
Yeah, I'm honestly not sure about this. If you use a tag to get a +2 bonus on a consequence, there is no FP's handed over but if you spend a fp to get a +2, you do hand over a FP. So I'm going by that(but not saying that's the correct interpretation).
Really, it's a hazy line between "the NPC" and the GM. I think it's more fun to keep FP's moving, so I'm inclined to agree with you. But I was pretty sure that if no FP is offered up, if none are exchanged.