It's true that in almost all situations, payments are applied to interest first and then principal. It doesn't really matter anyways, because the interest is capitalized (meaning, interest is charged on the interest) at the same interest rate as the principal, so it's six of one half a dozen of the other - either way the balance ends up the same.
That is generally true. But the exact dates when interest accrues can make a big difference on certain type of loans. On your mortgage for example there are some loans that apply interest on the 1st of a month, some on the last day, and still others that apply it based on a 30 day month or 360 day year. The days can matter because it can effect tax issues for some people, for example if you have to balance quarterly estimated payments with net income. It can also mean you miss the deduction on December interest for a full year. The OP is possibly in one of these special situations.
Bichon used to work in financial aid (I think he said that) so I'm inclined to think he knows what he is talking about. I also don't know how you could possibly get a deduction for interest you never actually paid or that was refunded on a returned loan.