Please correct me if I'm wrong but SQLite database could be downloaded from web-browser. There is a some ways to prevent it by keeping db files above www/ dir or via htaccess, however what you will do if you have only limited access to www/ folder and .htaccess aren't supported?

The server you are describing I have never seen... even in the 90s. I have never seen a server where .htaccess was disabled AND you couldn't go one level up from www/public_html/htdocs/etc.

So now curiosity has gotten the best of me... is this a private lan or something? The only thing I can think of it is one of those situations where a University gives you a website but it is really really locked down.

Also, try starting it with a dot (".mytest.html") as a lot of servers prevent hosting up files that start with a dot.