if you have a printer directly expose to the Internet, then you also are allowing anyone on the Internet to print anything they want in your office, using up paper and toner, wearing out the printer. That seems like a rather significant problem in and of itself :-)
firewalling also won't really help the identity theft example given (it may make it a smidge more complicated), because all that you need to do is to have the printer store the document and the second computer can retrieve the info later
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