What I said is correct.
For example, suppose for simplicity's sake, you have a 12" twist and a 12" barrel. A bullet fired at 1000 feet per second left moving at velocity that covers one foot or one complete rotation per millisecond. A bullet fired at 2000 feet per second has left the muzzle traveling at velocity that coverst one foot or one complete rotation per half millisecond. The first bullet makes one complete rotation in 1 ms, while the second makes 1 complete rotation in half that time. The second bullet is therefore launched at twice as many rpm as the first bullet was. To get to twice as many rpm, it had to undergo twice as much average rotational acceleration, just at the forward velocity of the bullet means it underwent twice as much average linear acceleration.
Where P is the twist pitch in inches, the formula for bullet RPM is:
RPM=MV×720/P
The 720 constant takes care of converting the mixed units of length (feet in velocity and inches in the pitch) and mixed units of time (seconds in velocity and minutes in rpm). The main thing you need to see is that rpm is proportional to velocity and rotational acceleration is therefore proportional to the linear acceleration that gets the bullet to that muzzle velocity.
I suspect the fact the same twist will stabilize the same bullet fired at different muzzle velocities, confused you into thinking the same RPM was stabilizing the bullet at different velocities. That would not work, even if a barrel could be designed to do it. In the supersonic range, at about mach 1.5 up until around mach 5 (faster than we fire bullets) most modern bullets experience a fairly linear increase of drag with velocity. That is caused by air resistance which increases with velocity, and is what pushes a bullet nose off course and makes it tumble. Therefore, if your bullet shape is such that it experiences twice as much air resistance going twice as fast within that velocity range, you then need twice as many RPM's for the bullet to have the gyroscopic inertia to resist being turned to tumble. Hence, the same rate of twist works with it at both muzzle velocities, because it provides that doubling of RPM with doubling of velocity.
In the real world, doubling velocity doesn't quite double drag of a modern pointed bullet in that mach number range, so increasing velocity with the same barrel twist rate will actually increase stability a bit, but it's not a vast increase.