You're right that it's about trust, but there's no real equivalence to that situation. The DM will never take the fates of a group of NPCs as seriously as the players will take their own characters, and they know that. They're not going to look at a bunch of prisoners under their care as personifications of the DM, and let that guide their thinking in regard to care or lack of care, nor will they see it as setting any precedent for their own care in a similar situation...
Personal experience tells me that "never" is too strong a term - I've seen the scenario play out more or less exactly the same way I described it more than once, with a GM having NPCs engage in surrender/parley first as a way to massage expectations. Certainly, players understand that PCs are more dear than NPCs, but the idea is to use the scenario to 1) gauge existing player expectations (do the PCs engage in surrender scenarios at all? if so, how?) and 2) set up later instances with the positions reversed.
But frankly, I don't think it matters about the specifics on HOW a DM gains player trust - that the trust exists at all is most important.