I agree with what you say, and would like to point out that being partially replaceable is also a virtue.

It is said that a good manager is judged in his absence. Furthermore, really good ones don't seem to be doing much at all. My point that while being wholly replaceable is a virtue, as you described - but being partially replaceable is also a virtue, to any small degree of replaceableness.

While Anne could either obfuscate the DB to gain job security and create pains for her replacement, or clearly document it and put her job at risk - either are problematic. What if she has a family? Supporting your family is also virtuous.

What she can do is find the sweet spot and mostly-win on both counts.

Anyhow, having the capability to make yourself replaceable if required tends to make you much more valuable to an organization from my experience - and would actually raise your job security. So, usually its a win-win to be replaceable and wouldn't hire someone who thinks otherwise.