I'd argue that ffmpeg belongs to the platform in a YouTube like usage scenario. Compare with ActiveRecord in Rails: Everything single thing your apps does depends heavily on it, yet, it's still just a piece of infrastructure.
It boils down to interpretation of what constitutes a "derivative product". I think it would be better if whoever used Rails and made changes to Active Record _had_ to share these changes (a-la AGPL), without having to share the app they built on top.
Similarly, it's better if ffmpeg users who offer a service based on ffmpeg were required by the license to share their ffmpeg modifications (the way Google already does without being required to) without a need to share the rest of the webapp.
> I think it would be better if whoever used Rails and made changes to Active Record[...]
But doesn't it at this point boil down to an academic argument? Surely Rails benefits massively from being popular, and draconian (which I consider AGPL) licenses might hamper its popularity. I doubt that Rails misses out on significant contributions just because they are not required. Contributing to open source looks good on a CV/employer branding page.
Platforms are a special case, where it is usually desirable to distinguish between the platform itself and stuff on top of it. That's why we have the classpath exception for Java: http://en.wikipedia.org/wiki/Classpath_exception#The_classpa...