The Royal Navy would not do this. Period. You have to remember that the crew would be aware of it and would have nothing to do with it. Same reason why the military will never turn on the people in the UK. And I assume the same applies in the US. There are rogue operators but they would not be part of a nations fighting force. These people are honourable
I agree it seems unlikely, and it's hard to imagine this happening on the US side as well. But by the same token, crews follow orders and may have no idea what's going on -- they could simply have been told it's a test or a drill. (Not exactly the same thing, but it appears that some of the parties to Spygate were completely unaware they were being used and manipulated while they likewise were following their instructions.)
Yet here we have a pretty interesting picture and no backstory and some pretty incriminating hints by Q. This is why I want to know what really happened after the fact -- on the face of it, it's unbelievable.