No, it means stability against deliberate changes. I.e., you will not have to change your nginx config between updates, unless there is a bug (and in theory upstream promises to reverse any accidental changes to configuration formats in the next patch release).
This is usually what people who actually do software releases mean when they say “stability”, there’s no realistic way to guard against actual bugs - otherwise you’d just not release the buggy software in the first place.
NixOS/nix do mean that your recursive dependencies can be pinned to anything, but you still often want stability from the software you directly depend on, so NixOS needs versioned releases. You don’t want to have to figure out a new nginx config format when there’s a critical CVE that allows RCE through opening your home page.
Desktop users often care less because glossy GUIs can largely auto-convert configurations and do fun popups that tell you about significant changes and such, but that’d be wholly inappropriate for unattended servers, which are a big use case for NixOS (probably the more common and polished use case, in fact, we desktop users are frankly weird nerds).