I'm not saying that view is necessarily good, but I think it's common. I also think it's quite common that people assume this is the client view and act accordingly.
I definitely think skipping testing with the goal of getting security patches out sooner is a terrible plan except maybe in the case of an active exploit. You can get both frequent patches and high availability.
This discussion is based on a false dichotomy. Yes, shops can be bad at updating dependencies. That's a matter of culture. Technically, I shouldn't have to constantly scan my dependencies for updates, much less security updates. That's what CVEs and release notes are for. Not freezing the dependency tree in CI and production on account of security updates is a bad pattern.
I won't say it's ever good, but for most software some downtime isn't the end of the world, certainly better than having security exploits available.