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No, that is not true. A massive object can never have speed c, even for an "instantly short period" (whatever that means). The speed of an object crossing the event horizon has nothing to do with the escape velocity. Saying that the escape velocity of a black hole is c simply means that no massive object can escape from the black hole, going awasy from the black hole. That has nothing to do with crossing the event horizon going toward the black hole.
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