Absolutely false.
Noting here: Ballistic Coefficient = Sectional Density / Form Factor, which, of course, Sectional density = bullet mass / diameter^2, where the Form Factor is a ratio of the coefficient of drag for the actual bullet versus a standardized projectile profile.
So it’s false to say ballistic coefficient is not directly dependent upon bullet mass. The form factor - the relative drag coefficient ratio - is influenced by length, but length is not defined variable within that calculus, it’s a ratio of measured drag coefficients.
What you are saying is true, of course in that ballistic coefficient depends upon the bullets mass, its diameter, and its shape (form factor). But it is also true that for any given caliber the longer, and therefore heavier projectiles, do have better ballistic coefficients and therefore better long range performance and less susceptibility to wind drift. But being longer, they require faster spin to stabilize.
For those who are interested in how twist rate relates to bullet length, bullet diameter, and bullet mass, take a look at Don Miller's stability factor and twist rule:
https://bisonballistics.com/Miller-...ist-An-Aid-to-Choosing-Bullets-and-Rifles.pdf
If you know your bullet's actual caliber (diameter in inches) which is .224" for 223 Remington/5.56x45, the overall length of the bullet (easy if you hand load, but available for many bullets on JBM ballistics), and its mass in grains which is printed on the box, you can calculate a "stability factor" for any given rifle twist rate with the following formula:
s = 30m/{(t^2)(d^3)(l [1+l^2])} which is formula B in the pdf article
where: s is the Miller stability factor, m is the bullet mass in grains, t is the twist rate given in calibers/twist, d is the caliber, and l is the bullet length in calibers. Note that the twist rate and bullet length are in terms of calibers. If you want to use the more common twist rate in inches/turn and bullet length in inches then you need to use the following conversions:
T = t*d and L = l*d where T is twist rate in inches/turn and L is bullet length in inches.
What is clear from the formula is that bullets of greater mass have a higher stability factor and those of longer length have a lower stability factor. What is not immediately apparent because of the way that twist rate (t) and bullet length (l) are expressed in terms of calibers is that bullets of greater diameter also have a greater stability factor. If you do the conversions T=t*d and L=l*d and do some algebraic rearrangement, the bullet caliber "d" winds up in the numerator.
The stability factor also assumes a muzzle velocity of 2800 fps and "standard" ICAO atmospheric conditions at mean sea level. It is easily adjusted for different muzzle velocities and different air densities as described in the article. The adjusted stability factor must be 1.0 or greater for the bullet to be stable gyroscopically and fly point first. A minimum stability factor of 1.5 is recommended and if shooting in very cold, dry, dense air at low elevation is possible, a minimum stability factor of 2.0 is recommended.
You can use the stability factor to compute a minimum twist rate by using equations C where T is the barrel twist rate in inches/turn:
T = {30m/[sdl(1+l^2)]} ^ 1/2
So if you want a minimal stability factor of 2.0 you can set s = 2, plug in "m" in grams, "d" in inches, and "l" bullet length in calibers and find your slowest acceptable twist rate.
Berger has a calculator to compute the Miller stability factor pretty painlessly but to use it for other than Berger projectiles you will need to find the bullet length elsewhere or measure it yourself.
https://bergerbullets.com/twist-rate-calculator/