@samwilson I've had the same issue, but it's been quite a while since I used Google Docs. I think Google Docs overrides the default copy paste and it needs elevated browser permissions to perform the action. Have a look around for which permission it needs.
@dean Yeah on further examination it appears to be when you paste HTML (or maybe any non plain text). But when the supposed HTML is just text it feels pretty wrong! I don't use Google Docs enough to care to install anything special though. :-)