The truth is that both of you are right. It's just a typical "check airmen" debatable topic because they have nothing better to do. There are no winners to this argument and let me explain why.
Suppose you go to an airport that has an obstacle departure procedure. Suppose you takeoff from runway 5 and it says in the OBS DP to not make any turns before 1000'AGL. Then when you line up and get issued takeoff clearance, the controller tells you to be at heading 035 at the runway departure end. What do you do?
The book answer to that, is, you comply with the takeoff clearance. Reason is, that the obstacle DP is available when there is no one to take responsibility (or as we like to call it in our law suit loving country - liability). If there is no tower (i.e closed), if there is no radar and your are in IMC then the OBS DP would apply.
Going back to your question. The answer to the check airmen is trifold. The initial approach fix is a good aid, just like everything in the IFR system is an AID. An aid to achieve the purpose of not hitting anything while being IMC. If you can come up with a combination of alternate means of avoiding terrain/obstructions be it, using grid MORAs and somekind of a race track pattern over the outer marker to lose altitude or anything of any sort you are golden. When you are lost comm, you are technically an emergency airplane. You might not call it that way, but the controller is giving you priority whether you like it or not. In lost comm you will do everything possible to the extent needed to meet the emergency and get out of it alive.
You want to use IAF, use it. Your check airmen doesn't want to use it? Don't use it. Its irrelevant. It's a total class room debate that really does not apply in reality.
If you flew a limited cessna 172 and couldn't reach grid MORAs and only had low airways and feeder routes to IAFs available to you, then that's one thing. If you have a jet capable of climbing to FL410 and come down in an instant, it's entirely up to you which set of rules you want to follow in order to maintain clearance and stay alive.
Two words. STAY ALIVE. That's the whole theory of IFR. That's as simple as you can make it.
Don't hit mountains, don't hit buildings, don't hit other airplanes. If you can reuse your own airplane afterwards it's a bonus.