No offense, but I shouldn't have to justify base rules of the game with any sort of narrative. It doesn't matter whether I say "I deftly lunge and cut the back of the giant's leg with my sword, hitting a tendon with enough pressure to force him to step backwards; he takes 18 points of damage and is pushed one square." or "I hit the giant for 18 points of damage and he gets pushed back one square." The rules state the giant gets pushed back - DM or not, I don't believe that someone can ignore a power's effect on the grounds of narrative. That is lousy DMing - it's like saying you don't deal damage unless you come up with a good enough narrative to justify the damage you did.
My DM seems to have his own ideas about the game world and dislikes how the rules "dumb things down" instead of applying "common sense" (both actual phrases he used). For instance we had a case last night where I used a pushing power to knock a Demonweb Terror off a bridge that fell into a 100+ foot drop. It was at the edge and I hit it with Tide of Iron; DM rolled its falling save per the rules, and failed. He got upset ("Can you imagine how hard it would be to knock a spider off a ledge?") but he let it slide.
I was siding with you at first in this discussion, but the more I read things, the more I think both you and your DM are "wrong" (in a way). I think the two of you need a perspective that's between the two of you.
Based on what you've said, it sounds like your DM might have a 4E bias. He feels like it's become too much about tactical powers and that there is a loss of realistic narrative that he may resent. Though I believe he's mistaken in that belief, he's being literal as a way to resist the style of play that he *believes* 4E enforces.
On the other hand, you seem to embrace the mechanical and tactical aspects of the game, and don't want to have the mechanics to be held back by the narrative.
I think that the thing that your DM may not understand is that 4E completely reverses the way that powers are approached. In previous editions, the narrative effect of powers was often the focus, and the mechanical parts were created in order to help describe the narrative effect (often with disclaimers, rules, and limitations to prevent abuse through altering the narrative). 4E completely turns this on its head and gives lots of mechanical abilities with a suggested (but not absolute) narrative.
He is being inflexible on the effect because he seems to be seeing narrative as static, instead of realizing the effect is static and the narrative is flexible.
On the other hand, you are being inflexible in that you think that the narrative shouldn't be required to support the mechanics, when this is clearly what is intended in 4E. You have pretty much said that you don't care about the narrative effects, and that the mechanical effects should be followed through to the letter, else it unfairly penalizes you. While I agree that it unfairly penalizes you, I don't agree that it has to be followed even if it makes no sense in the situation. I think you and your DM need to meet in the middle on this one.
My suggestions for the player are to suggest a narrative and asks the DM if that's reasonable. Another way is for the player to ask the DM (or even the other players at the table) for suggestions as to what would make the narrative more reasonable. You've already stated that you don't like this idea, but it's hardly fair to the DM to imply he's lazy and stubborn while not willing to contribute to the story and yield some yourself.
Regarding the DM, I don't really like the idea of pulling DM fiat and just forbidding or restricting a power as you've described. Instead of the DM flat out saying that it doesn't make sense, he should ask the player, "can you describe this in a way that makes sense?", or "how would you feel if we describe it like __________ instead?"
Being able to do this is what I love about 4E, and both of you really seem to be missing this concept as a gameplay tool.
