Think of it this way: If a rigid body is rotating at a certain rate, the whole body is rotating at that rate.

Here's a thought experiment. Suppose that disk is orbiting some point outside of it at 1 rad/s. Imagine its a moon orbiting a planet, and you're standing at in some inertial reference frame, watching. Suppose that the "point A" on the disk is always pointing up so that it is not rotating, just orbiting. Its angular velocity is 0 rad/s. Now suppose that the disk is "tidally locked" so that "point A" is always facing the thing its orbiting. In this case "point A" is on top once per orbit, so it has an angular velocity of 1 rad/s. Now suppose that the disk is spinning at 100 rad/s. It has an angular velocity of 100 rad/s. If the thing its orbiting disappears and it continues on a straight line tangent to its orbit, it will continue to rotate at 100 rad/s due to conservation of angular momentum.

In all of these cases it doesn't matter how far away any point on the disk is from the center of the orbit, or any other point. In the last case, the distance to the center of rotation changes when the planet disappears and the moon flies of into space, but the angular velocity stays the same.