issue is they weren't betrayed. Or even slighted by the human city. The city was acting in good faith, which they knew. And the reason they had trouble paying them was cuz Nagash kept assaulting the caravans, which they also knew. And to which they responded by sending a bigger escort of fyreslayers with the next set of caravans cuz every single caravan was escorted by fyreslayers due to their importance. All of which was stated in that short story. Also, weirdly enough despite this caravans being completly fyreslayer controlled simply handing over the ur-gold to the caravan didn't count as having paid. For some inexplicable reason it only counts if the gold actually makes it to their mountainhold, despite the wellbeing caravans obviously not being under the control of the city.
Hence what ultimatly ended up happening is that they betrayed their employers, mid-battle, simply because Nagash offered to pay them more. And they then soothed their conscience with a flimsy excuse. There was no betrayal, or slight, from the city, and Nagash didn't even trick them. Hell, I don't think there was even a real argument among the fyreslayers themselves if they should take this bribe or honour their oath to the city.
O, and not just that, but the emmisary of Nagash asked them to simply step aside, they didn't have to continue fighting. Instead they joined the Nighthaunt in slaying their former employers. Cuz you know, having betrayed their former employees they might as well try to take the remaining ur-gold from their vaults. And got slain themselves in a form of karmic retribution.
Based on this story their oaths are completly worthless. Hell, there's a short story in a recent white dwarf about some ogers who got bribed to defend a city with food and even they had a better justification for their eventual betrayal. At least their deal actually got ruined.... And being less trustworthy than ogers is kind of impressive. It's just one hell of a weird story, but not weird enough to clearly be just a "bad" story by someone who doesn't know fyreslayers.