Objects falling into a BH will be accelerated relative to an outside observer to near light speed, however the definition of the actual speed is a local one and will depend on the coordinate system used.
In the Painleve space-time, which is the frame of an observer falling into a Schwarzschild BH from infinity, the velocity of the faller reaches c (wrt to the BH) exactly at the horizon. Which is nice and symmetrical.
The good news is that the relative velocity of the event horizon and a particle falling into it when the particle crosses the event horizon is always 'c'.
The bad news is that it is not really correct to think of the particle as being accelerated up to the speed of light. The worldline of the infalling particle is known as "timelike" - this is a characteristic of the worldline of all particles, and is different in nature of the worldline of light, which is "null".
The event horizon is a null worldline (or a collection of them, to be more precise). In fact, you can think of the event horizon as trapped light.
So the worldline of the infalling particle never changes its timelike nature, and the reason that the relative velocity between the event horizon an the infalling particle is equal to 'c' is that the event horizon is lightlike rather than timelike.
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