First off, with a bullet, it is not only pushing through the air, but also spinning rapidly on its axis. Mass, inertia, torque, and other factors are in play. Bullets are essentially pointed rods thick at the back, thinner at the front. So a tiny change that does actually unbalance the front is over-ridden by the still balanced stability of the more massive rear section.
Anything less than a perfectly balanced nose will "wobble" it's something that could be calculated, math says it must exist, but the effect of that tiny wobble is (usually) hidden /overwhelmed by other factors, so there is seldom any effect on accuracy we can see.
An "unbalanced" bullet base, on the other hand, has a great effect. It is the greatest mass of the bullet, so if the weight is lopsided (not "true" with the spin axis) the bullet won't fly true, either.
This is all correct.
Two things to consider, or so...
That slightly deformed tip actually takes only the tiniest bit of material and puts it off balance, right there at the axis of rotation. With the spin of that massive bullet, the thing is going to be stabilized based on all the rest of the lead. That little bit of skewed weight at the end of the axis can't possibly upset the stability of the rest of that mass. Not that it would really matter, as shown by the football, even if the nose started to rotate the body (center of the mass) would still remain stable (in relation to itself) in space without being affected.
While some people would think that friction would affect the bullet adversely, that air would push it aside, much like the spoiler on a car, once again, we have so little deviation that could be caused by the friction that it wouldn't be able to push the bullet off of axis. Again, pushing it off of axis would not result in the bullet taking another path, it would just cause the bullet to "wobble". Since it is also rotating, it also has to be pointed out that if the pressure or imbalance is on the 'outside' of the rotation, it's going to just guide that deviation back to center. Unless the damage causes deviation outward from the axis, there won't even be a reason for the thing to destabilize from the axis, it will self correct.
As was said, it has been tested, and casual testing showed no deviations. If you set up scientific conditions and tested it in the most extreme distances, there still may not be any deviation that would show when compared to bullets with perfect points.
As we have read, yes, damaging the base where the mass is located can cause the bullet to have problems. First, a chunk of missing base material causes the bullet to leave the bore with a 'poof' on one side, causing a tiny bit of instability. Friction at outer edge of the base can cause the heavier base to destabilize a bit. with both wind drag and a weight being off center of the axis, any deviation at the edge and towards the center of the mass will be more inclined to push the axis off.
Look at someone whacking a golf ball. See how the dimples make them go on wide, arching flights? The dimples on the bottom are resisting the air that they are flying into. The dimples at the top are not having to resist that pressure. The dimples at the bottom actually function like a wedge, or ramp, as the dimples are forced through the air, pressure against the dimples on the bottom push on the center axis of the ball. This will cause the ball to climb if the ball is rotating backwards.
Regardless of what direction the ball is actually flying, it will follow a straight (mostly) line perpendicular to the rotating access, just like a gyroscope.
Let me be the first to assure you that whacking a bullet with a golf club isn't going to answer any questions. It will just waste a lot of bullets.