Completely incorrect. BC is all that matters when calculating external ballistics. The mass of the bullet divided by the square of the caliber determines sectional density and sectional density factors into the ballistic coefficient. As such, all that matters about the bullet mass (it proportion to the frontal area of the bullet) is captured in the BC. Wind deflection is a drag function. BC is the drag model of the bullet. Wind deflection is modeled with BC.
The flaw is thinking is that the BC determines the drag force on the bullet. The BC determines the drag acceleration on the bullet already normalized for bullet mass. As such, weight doesn't matter; if you have the BC, you have all you need to know about how the bullet will fly.
If you want to run a little "look see" run two bullets of different calibers and weights with the same BC through a ballistic calculator using the same MV. The ballistics will be identical, to include wind drift.
As was stated before, a ballistics program uses a simplified trig and physics problem to approximate what's actually going on, under what would be considered "ideal" conditions. You running two different bullets through the same calculator and coming out with the same answer shows nothing more than your program can work the math correctly.
When wind is calculated into that program, it assumes a steady wind from a constant direction. You won't often find that in the real world. Any change in wind or gust is going to buffet the bullet in flight. A heavier bullet will be affected less. It's simple physics.
Again, the very definition of BC shows that it will not usually remain the same for a heavier and lighter bullet. Since the calculation is done with mass and diameter (which remain the same) and drag coefficient (which is a function of velocity), it will change throughout flight. The ONLY way that a heavy and light bullet will fly the same trajectory is if they have exactly the same sectional density, and their drag coefficient changes exactly the same amount as the velocity decreases (or if they have different sectional densities, but the drag coefficient changes at a set ratio which offsets their difference in sectional densities). Obviously, both of those cases are aerodynamic flukes, and a pair that actually does that would be extremely rare. Here's some ratios on that effect:
Two bullets have the same ballistic coefficient at an identical velocity. The sectional density of bullet two is twice as great as that of bullet one. They experience the same change in drag coefficient as velocity drops. The ballistic coefficient of the bullet with the smaller sectional density is affected twice as much as that of the larger SD bullet. The smaller SD bullet is now losing velocity faster than the higher SD bullet.
You are correct about bullets turning into the wind. However, that only takes into account a steady state wind condition. It does not take into account varying wind and gusts throughout the bullet flight. Even though ballistic coefficient takes into affect drag acceleration, it does not take into account center of gravity and moment of inertia. Both of which will determine how fast a bullet can "turn into the wind". The mass and shape of the bullet are the only things that determine CG and moment of inertia. Therefore, they will in some way determine how much the bullet is affected during the time that it faces lateral forces before it can turn into the wind.
Again, ballistics programs are a very good estimate. However, there are numerous reasons why they are not completely accurate in the real world. When you leave the realms of simplified trajectory programs and enter the atmosphere, bullet weight will have an impact, albeit a small one.