Not necessarily. If you have cloud synchronization turned on, then every file you work with might be copied to Adobe's Document Cloud, but it would only be available to your account.
When you email the document as an attachment, and it's then opened in the mobile Reader, the document will be stored on the device (phone or tablet).
What exactly does the message say? I don't think I've ever seen anything referring to a "public file".
You may want to consider using a solution that is more geared towards signing - take a look at Adobe's "Fill & Sign" app.
Karl Heinz Kremer
PDF Acrobatics Without a Net
PDF Software Development, Training and More...
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