I may also be misinterpreting, but afaik it’s how close any given component is to the 2.500 2.495 V ideal voltage out of the box, not how it behaves when running (that’s more temperature drift etc). This matters if you’re doing large scale manufacture and are willing to pay a bit extra to avoid having to manually trim your gear, but unless I’m missing something we’re not quite at those volumes here 
@antoine.pasde2 talked about it here:
(I mean, it is labelled as a *precision* reference and there’s even an example that shows to use it to make an LM317 more precise in the datasheet, which wouldn’t make that much sense it it was worse than the other regulators )
Still not sure about headroom, though, so needs testing. Looked a bit more and found some AMS1117s (LM1117 variants), but still no TL431s.