There are 3 relevant questions that need to be asked and at least plausible answers provided.
1. Why shoot it down? The aircraft was heading into French airspace and the only area or site that might require it was stopped quickly is the French nuclear reprocessing plant at La Hogue. Anything else and it becomes a French problem and their decision.
2. Who would authorise the shoot down? It has to be a political decision, no serving officer would have authority to order engagement of an aircraft that represented no threat to the UK even if the US authorities requested it. It is just within the realms of possibility that they might accede to a French request to do so if they were unable to deal with the situation themselves. But it would almost certainly require US agreement.
3. How would the intercept be controlled and by what means would the authorisation to engage be promulgated and relayed to the interceptor? There’s now a long chain stretching back to Wattisham, High Wycombe, MoD, Foreign Office, West Drayton, CRC et al. That’s an awful lot of people in the know and this is a quite exceptional event.
BTW I don’t believe in Conspiracy Theories but readily subscribe to the C**k Up Theory.
Answers on a postcard please.
YS