Web application document storage

This is really a yes/no question in which I believe the answer is fairly clear, but I'm just making sure here. It's taken me awhile to come to this conclusion so hopefully this will be useful to others.

My belief is:

A document-based web applications (think Google Docs) cannot save locally to the hard drive in the way that desktop applications can, i.e. with a persistent connection to the file such that the user can hit save to update the file. This is due to important browser security.

So, you either have to do what Google Docs does and save to the cloud, or save to some other database on the server, or write a desktop application, perhaps something like Electron HTML/javascript apps that are really desktop apps.

While web applications can download a file, and can even invoke a save-as dialog, they cannot persist the connection in the background in a way that can give users confidence that their file is updated automatically or whenever they hit save. At least not without additional software installation by the user.

Is this correct?

Also, I may not be using the right terminology: feel free to correct it.

Thanks.