Firstly, it's a bad idea to do it exactly like that anyway: Instead set up a folder off your root called (say) "Users" and put the files in there.
If you just put user files in your root:
User: "User1"
File: "User1.html" or "user1.aspx"
Then what happens when someone logs in as user "Login" or "Default"?
If you use a separate directory, then that should work a bit more securely.
Next The way I would do it (being the suspicious type I am) is not to provide them with direct access to the server file structure anyway: To load a file, paste it into a text box, and then your software files that under the user name with the appropriate extension.
I would also consider keeping each user file in a separate directory (under "users") called his username, with a custom web.config that allows access to you and that user only - so they can't faff about with each others files.
So you would end up with:
\ All your files for the site
users Folder
User1 Folder
web.config Limit access to you and User1
User1.html The file they loaded
User2 Folder
web.config Limit access to you and User2
User2.html The file they loaded
...
[edit]I forgot the web.configs...[/edit]