No one has been in a black hole so this is just my assumption.
I will try to explain you with an example that was shown in Genius - A web series shown on National Geographic channel.
The example was given by Einstein himself. So, I am going to explain the example in Einstein's way. Suppose, there is a hill which has a railway track in front of it. You are standing upon the hill and you notice that two lightning hits the ground. Now for you, they hit at the same time because you were outside the object. Now let's get inside the object and recall the striking of light on earth. Suppose a train is traveling at 200 KM/h. You are looking out of the window and notice that lightning didn't hit the ground at the same time because when the first lightning hit the ground the train was nearer to it but now it is moving away from it that is towards the second lightning. So the frame of reference got changed when you were inside the train.
Did you notice the difference? When you were upon the hill, the distance between you and the lightning was equivalent therefore it seemed to strike at the same time but when you were in the train lightning hit the ground at different times.
Same thing happens when an object is inside the black hole. The frame of reference is different for an object inside the black hole to that of an object outside the black hole.
Therefore, I conclude that Einstein's theory of relativity holds true inside the black hole.
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