The vulnerability only exists in applications that allow a potential attacker to run arbitrary SQL. If an application allows that, it is usually called an "SQL Injection" vulnerability and is the fault of the application, not the database engine. The one notable exception to this rule is WebSQL in Chrome.
I put up https://www.sqlite.org/security.html recently to serve as guidance for people who want to live on the edge and give unrestricted SQL access (or unrestricted database file access) to potentially hostile attackers. That page is a work in progress. More could be said. For example, it is probably also a good idea to use various obscure APIs to limit the length of SQL statements or the amount of memory that can be used, to avoid DOS attacks. I'll keep improving the document as I have time.
Our intent is that SQLite should be secure against these kinds of attacks. We have spent years fuzzing it to try to find these problems. But the thing is, we never configured a fuzzer in such a way that it might start modifying the shadow tables of FTS3, and so we missed this one. Moral: never underestimate the ingenuity of a motivated gray-hat.
The Chrome people have recently starting fuzzing SQLite database files on Google's infrastructure. We had previously only fuzzed database files on our own workstations. It's amazing the number of new problems you can find when you run a fuzzer at scale. :-) A few more problems have been fixed. We are not aware of any exploits. And in particular, if you follow the advice of the article above and "PRAGMA quick_check" untrusted database files or set "PRAGMA cell_size_check=ON" then none of the recently found and fixed issues are reachable.