On proprietary platform:

What if:

1. The web service software is proprietary, and there is neither api nor web UI function to export your data. And its EULA said you cannot modify its javascript/css when browsing it, or auto fetch and parse its HTML via curl or other similar tools or programming languages.

2. The web service software is licensed under Free Software licenses but there is no api and there is no export your data function in web UI.

3. The web service software is proprietary, but it has well designed api exposing all or more functions in its web UI.

I won't discuss 1. I think it is Proprietary from any aspects of view.

But what about 2 and 3:

Software:

Proprietary: 3; Free: 2.

For someone who wants to host a web service:

Proprietary: 3; Free: 2

It is consistent till now.

But for someone just wants to use the hosted service, do they have more freedom when using 2?

I think the result is mixed:

1. 1 does provide the freedom that the user can host the service on their own machine or on their friends' machine.

2. But for manipulating their data, 2 (Proprietary Software) provides more freedom than 1 (Free Software).

Traditional local free software does not have this issue, since it runs on your own machine. If a free software cannot save the result to disk or pipe the result, you can edit its source.

A program is free software if the program's users have the four essential freedoms:

The freedom to run the program as you wish, for any purpose (freedom 0).

For web services, there should be something like a freedom -1.