To clarify again... the objects will actually stretch, as well, as they get "close enough" to the black hole such that the acceleration due to gravity at their feet is significantly greater than the acceleration at their head (or whatever, I'm assuming the feet are pointed "down" toward the black hole). This would be readily observed by anything close enough to see the thing getting stretched. This has nothing to do with GR, per se. It only has to do with feeling different forces across a body. The net force causes acceleration, which increases (theoretically without bound as you get closer and closer to the singularity) and will eventually rip apart whatever bonds are holding that body together - intermolecular bonds, then molecular bonds, then atomic bonds... who knows how far this goes. No point in dwelling on it. QM and GR don't really get along at these energy scales.
This stretching may happen inside or outside the event horizon. This is because event horizons have to do with the magnitude of the net (not necessarily exclusively gravitational) acceleration, whereas the stretching is due to the variation in g-forces (accelerations of a mass due to gravity) felt by objects which occupy some volume.
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