Bullet arch path, and sight line of view threw the sights.
The bullet never rises above it initial flight path (bore line of the barrel), its just the bullet is shot at a upward arch to allow gravity to pull it back down to strike the target at the desired point/distance. Since the sighting plain is above the bore line, then the sight path will be looking down and intersect with the bullets travel in space at two different points. Often, when referring to sighting in at short ranges, the bullet is referred to as climbing, but in fact, its the increased angle of the sights to looking down to intersect the bullet path at the shorter distance that is being referred to.
P.S. The last small arms bullet that I am aware of that had to ability to climb, dive, go both right and left of the bore flight line was the one used to kill JFK. Since I’m not buying the ricocheting story given by the goverment, my guess is that this smart bullet/ rifle was invented and produced at Area 51 way back. Now some years later since the military is "designing" rounds that are smart (can do just that), maybe the bullet/ rifle has already been issued to black ops/ people in the know, and they are designing a cover story to one day release it the public sectors of the government.
[Just another conspiracy theory, and that possibility that that your friend are in the loop regarding the truth. The problem now that you have posted this information of the climbing bullet, have broken their cover, they may just have to take you out to conceal the secret. If you don’t post anymore, then at least we know what happen.]