The pays says: "Billions and billions of copies of SQLite exist in the wild". Which seems reasonable and is counting the number of installs as you preferred.

Later on the page says "it is seems likely that there are over one trillion (1e12) SQLite databases in active use" which is the quoted title and seems like a reasonable claim and is counting "documents" not installs.

I don't think "documents" is an uninteresting statistic. It is just a different one.

That's exactly what's being counted. A database is a SQLite document.

That's... Exactly what a SQLite database is - a file. This thread isn't about the number of unique devices that potentially use SQLite

"Active" is a big word here. Each of these databases is in nearly continuous use. You couldn't say that about the vast majority of excel spreadsheets, or any word documents.