A 28-year-old male with a 5-year history of duodenal bulb ulcers has recurrent melena and intermittent proton pump inhibitor (PPI) therapy. Four hours ago, he experienced hematemesis three times (total ~600ml) and passed black tarry stool (melena) three times (total ~200g), accompanied by marked dizziness, sweating, and palpitations. He had multiple episodes of syncope when changing from lying to sitting position. Which of the following statements about blood urea nitrogen (BUN) changes after gastrointestinal bleeding is INCORRECT?