At high alt the thrust is within 2-4 % N1 of max available, so any increase would have a negligible pitch effect if any at all.
Teaching students to close the trust is negative training, self-made procedure. The instructor should either explain what specific trick is he trying to teach and carefully insist the students understand its limited scope, or stick to the book script.
A general comment, all devout followers please note that vilas argues to close the thrust specifically in the presence of such an engine pitch-up moment that a nose down movement cannot be achieved.