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I don't think it's copying verbatim, it might be caching it for a short while but not saving it (based on what I'm reading about the technology).

So the more interesting question here: is a computer legally allowed to generate an original interpretation of text on a page?

The user of the app is still copying the text verbatim and transferring it to the server, which is distributing.

Not exactly.

A. They probably cache only for a little while B. They aren't republishing it

The company isn't. The user is still distributing.