So if I have everything straight, I would say he's half wrong. Per the commentary to 1026.37(o)(4):
1.Rounding. Consistent with § 1026.2(b)(4), except as otherwise provided in § 1026.37(o)(4), any amount required to be disclosed by § 1026.37 is not permitted to be rounded and is disclosed using decimal places where applicable, unless otherwise provided.
Loan Terms section: I cannot find anything in 1026.37(o)(4) that says you should round or truncate the amount disclosed for Monthly Principal & Interest amount in the Loan Terms section, even if the amount is a whole dollar amount. If someone else knows that reference, they will have to point it out. As far as I can tell, you did that correctly.
Projected Payments table: On the flip side, I can't find anything that says you can truncate the amount in the Principal & Interest line of the Projected Payments table unless you're disclosing a range of payments. Every other line in that table has to be rounded per 1026.37(o)(4), but there's nothing I can find directed at that line of the Projected Payments table.
Again, if I missed something, I apologize, but that's what I have found from reviewing this section.