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I’m not privy to the terms of your NDAs, so I don’t know the restrictions that you have agreed to. By nature of the service, Google is going to have to temporarily store a copy of any document that you print. According to Google, they do not retain a copy after printing is complete:
“Yes, but only for so long as the printing job is active and not complete. We have to do this to make sure your document gets printed. Once the job is complete, the document is deleted from our servers.” https://support.google.com/cloudprint/?rd=1#2541911