It is absolutely true that a work can be in the public domain and not have source available (or even contributable). But that doesn't really matter to most people. The question for most people is not whether something is open source, but whether they can copy and make use of a work without being held liable for copyright infringement. SQLite happens to be both public domain and open-source to an extent (i.e., source available).

Conversely, open source doesn't necessarily mean "free to use without encumbrance." There are many open-source licenses that forbid certain uses (e.g. Business Source License). On the other hand, a work in the public domain is free to be used by all without restriction.

A better analysis of open source vs. public domain would be in the form of a square, where one dimension would be the right to use the work, and the other dimension would be the ability to obtain and contribute source code.