I've always understood the explanation for running the "stable" or LTS variant of a particular distro to be also to minimize potential breakage when updating packages in regards to other software running on the machine. That is, the stable variant isn't going to do a full version upgrade of a package without a very good reason. This makes it less likely to get yourself in a scenario where you update your server (perhaps for a security vulnerability) and then find that you're web app or some other custom coded software then breaks because your update for security also updated a library. Additionally, a stable variant typically has security-only fixes from newer versions of a package ported back into the old version of that package carried in the stable variant.