Gale McMillian's often quoted theory:
By putting fore end pressure you are actually bending the barrel upward in an ark so that as the bullet starts down the bore it is trying to straighten out the gentle bow induced by fore end pressure and it holds the barrel against that force. This causes the bullet to exit at the same vibration point shot to shot even though there may be a velocity spread.
That's an easy myth to shoot holes through.
First off, there's no guarantee that a poor quality, non-stress reliefed barrel will always bend in the vertical axis when it heats up. Nor is the direction always going to be either up or down; it will be in the direction the stresses bend it.
Second, any fore arm pressure on the barrel will change with how the rifle's held by the shooter. From a fixed amount and axis when the rifle shot offhand where it's constant from shot to shot to any position that [puts pressure on the fore end changing the force axis and direction. That'll change how the barrel wiggles while the bullet goes through it and the bullet will exit at different directions depending on that external force and its axis.
Third, bullets leaving at different muzzle velocities exit the barrel at different angles. The bore axis at the muzzle's going through a narrow range of angles all the time as soon as it's fired. And the barrel will wiggle and whip at the same frequency for every shot fired regardless of how long it takes for the bullet to go from case neck to out the muzzle and from very cold to very hot. Adding a variable pressure to any point on the barrel will change the direction and amplitude the muzzle axis wiggles at but its frequencies will stay the same.
Gale McMillian claimed the Rem 700 box magazine recevers are stiffer than the Win 70 ones. People have bet him thousands to prove it but he never accepted the challenge. Folks who've measured how much each receiver bends from a given force know which one's stiffest.