You are correct and the expert here is mistaken. The expert has confused points with mortgage insurance (PMI or MIP).
If you pay points on a mortgage, and then refinance, you can deduct the remaining points in a lump sum if you refinanced with a different lender. If you refinanced with the same lender, you add remaining points to any new points and amortize the total over the life of the new loan.
However, for PMI or MIP, there is no deduction for the unused part of the up front PMI premium. You just lose it. (Essentially, you pay a premium to insure the bank for the first 7 years of the mortgage. When you pay the full premium up front, you can still only deduct it over 7 years, because you can't deduct an expense before it happens. If you refinance, that insurance policy is canceled and the bank gets to keep the extra premium; you can't deduct it because the insurance policy no longer exists.)
I will flag this for review.
