[Mercurae]

There are definitely two different styles presented here. One side is the RAW, strategy gamers who use all the numbers and rolls no matter what and play it straight. Then there's the story-tellers who fudge rolls or rule by fiat. Both are perfectly valid ways to play, it just depends on the GM and their players. Personally, I like both, it just depends on the game.

The important thing is to make sure the players understand which type of scenario they're in. Obviously, if they are thinking in terms of the former, doing the math, checking character and item stats, etc. then they're going to reach different conclusions. If they calculate that the hostage can probably take the hit and they can run over and heal them, they may just bite the bullet and attack. If the GM then said, "Nope, throat slit, they're dead", the players would definitely feel cheated and it would not be fun.

If instead the GM makes clear "You either let the baddie go, or the hostage WILL die", then the players have a very different decision to make. Rather than basing it on the rolls and stats, they'll think in terms of "Do we sacrifice a hostage to take down the bad guy or do we let them go and fight another day?" This has a very different feel.

These are two very different dynamics but neither is better than the other. Again, the most important thing is making sure the players know how the game will go. The GM should also keep the feel of the game consistent. If it's 90% hack and slash, stats, and gaming it out then all of a sudden none of that matters and it's purely a story-based decision, it feels very jarring and unfair.

That's all a very long-winded way of not actually answering the question and just saying it depends. Make the decision based on yourself, your players, and your game.