Web APIs change on the whim of the provider and have no permanent basis to build on. No one benefits from pretending that web APIs are as stable, composable, or as powerful as
proper files.
I italicized proper there because my real point is that you're simply defining yourself the win with the word "proper" and not comparing like to like. You can win any comparison by accounting for only the good of one proposition and only the bad of the other, but that's not a valid argument. If, for instance, we ask our web API to have some sort of assurance that it'll be there next year... hell, next week... suddenly "proper web API" turns out to resolve to absolutely no concrete noun at all. (How "proper" would you have called the Twitter API last week? You know, back just before Twitter started shutting huge swathes of third party apps out of it?)
But that's just one definition. The truth is you need the right tool for the job.
It is all, in the end, just bits. The bits don't have color [1], and they don't acquire color by being in a web API instead of a file.
[1]: http://ansuz.sooke.bc.ca/entry/23