How is this possible if the gravitational field of a black hole is so strong that not even light can escape?

The “out” refers to the region near, and outside of, the EH (Event Horizon), not to anything inside the EH.

When an object like a star falls within the death grab of a BH, then it becomes shredded and a large disk is formed. This disk revolves at incredible speeds, which makes it extremely hot and bright.

But this disk material will continue falling past the EH where it is lost to all observations by us.
I know that the theory says that this material that was thrown out "late" says that the material must have remained outside the event horizon.

But, do we have decent models for what it was doing outside the event horizon for (Earth) years before it was ejected? Shouldn't it have been emitting synchrotron radiation that we could detect - albeit maybe highly redshifted if emitted just outside the event horizon.

I am interested in this because I am seeing some issues with the way we explain light behavior at event horizons.