They address this directly under the section entitled "Open-Source, not Open-Contribution":
SQLite is open-source, meaning that you can make as many copies of it as you want and do whatever you want with those copies, without limitation. But SQLite is not open-contribution. In order to keep SQLite in the public domain and ensure that the code does not become contaminated with proprietary or licensed content, the project does not accept patches from unknown persons.
In other words, the reasoning is that since the code is released to the public domain, they want to ensure they can continue doing so without encumbering or confusing future releases with tainted contributions. Quite admirable.
SQLite is open-source, meaning that you can make as many copies of it as you want and do whatever you want with those copies, without limitation. But SQLite is not open-contribution. In order to keep SQLite in the public domain and ensure that the code does not become contaminated with proprietary or licensed content, the project does not accept patches from unknown persons.
In other words, the reasoning is that since the code is released to the public domain, they want to ensure they can continue doing so without encumbering or confusing future releases with tainted contributions. Quite admirable.