That's the key really. Supposing a terrorist training camp were found in rural Wales. If the RAF go and bomb them - perhaps there's no time to get police or ground troops into the area - is that an act of war by the British government against itself? Of course not. Now, supposing rather than an RAF Tornado, an American F-15 from RAF Lakenheath did the same (possibly even flown by British personnel: there are a few British F-15 pilots as it happens, though I don't know if Lakenheath has any) - act of war, or act of friendship?
Really, it's a question of whether we as a country identify with the terrorists, or those fighting against them. I think the fact the Pakistanis are angry about American troops fighting with the terrorists in Pakistan, rather than with the terrorists themselves, speaks volumes about their allegiance.