The quoted text in the OP is emotive given the mention of high speed and manoeuvres and leads us to think of amazing feats not possible in reality. However, if we break it down simply then we can start to see how it is possible.
As I noted above the bullets coming down would be slow (ie no longer ballistic) and unlikely to damage an engine............
............................. ........If by now you still don't get it, I have great deals on bridges.
Vulcan, your thinking is wrong sir. As Vraciu has tried to point out, you are failing to fully understand the vertical aspect of the equation.
As I read it your contention is that even if the plane and bullet could meet they would have similar relative velocities and so damage is unlikely. That is a flawed conclusion.
If I throw a cricket ball or baseball horizontally and try to catch up with it I cannot. However I can easily throw it with the same velocity and easily catch it if I change the angle I throw it to be more vertical and I use speed and manoeuvres to try to catch it. When it comes down it has less energy than when I released it but it will damage me if it hits me. I challenge you to stand under that ball and refute my statement.
Therefore it is equally possible to fire a bullet from an aircraft at a certain angle and have that same plane intersect the bullet coming down. I will leave you to do the math but I am certain that bullect could inflict damage.
If you do not get that I have a great deal on bridge repair kits. Let me know the delivery address.