The warning on 121.5 is exactly the same as happens with any 'armed guard' challenge, the law requires the giving of a warning unless there is no time to do so. In this case there was time, and you will note the warning was issued on behalf of the Govt.
The flight plan will assist with identification of an aircraft provided the contact is close to the planned or approved route. What it will not tell you (in the absence of comms) is that all is well on board. And if you have identified an aircraft via the flight plan and then the track behaviour is no longer as expected, you have an aircraft that is potentially hostile until it is proved otherwise.
The decision to engage is clearly a tough one but it will not be taken in the cockpit for a scenario like this. Let us assume 'the system' has decided the aircraft is hostile and has hostile intent. If you do shoot it down over an urban area there is a good chance of casualties on the ground, but there is also a chance wreckage drops into roads, parks, gardens etc. If you let it proceed to its target, you have absolute certainty of a terrorist success. Therein lies the difference.