...This is also why often times stronger opponents will feel insulted if you refuse to resign a dead lost position...
Just so we're clear, I agree with almost everything you said except the bit I quoted...
Dead lost has a different meaning for everyone, my idea of a dead lost situation is often different from that of the general public, and most certainly different from that of my opponent. If my opponent wants to get upset because I believe I have a chance to draw, he gets an opportunity to play me into a hole so deep I will struggle to crawl out because of the shame. And if he does get upset, I have an even better chance to find that draw 
What I'm trying to get at is actually this. It is silly for anyone to get upset because you choose not to resign. It isn't the opponent's choice to say you've lost and have no hope of recovery. He can carry on playing and prove you wrong. Of course if he feels he's not gaining anything by playing on he can resign or offer a draw, since if he's happy with the idea that he's won already there truly is nothing to gain for him by playing on. But for most people the win is what counts (especially if they like their rating). I've never heard of anyone winning a game by claiming a position "Won". If that rule existed most games would have 2 winners after 10 moves.
I am all for showing respect to your opponent and resigning at a proper time where you really feel the game is lost, but if my opponent asks me to resign or complains because I have not resigned, he better be ready to play until he has me in mate.

You resign when you are confident that your opponent has shown to you, either in a previous game or the current game, that they are knowledgeable enough to beat you from the current position. The continuation of play is similar to that of sticking around at a baseball game when a team is 10 runs down in the 9th with 2 outs and no one on base. Time to head to the parking lot! (Insert your favorite analogy!) And yes....of course there's a minute possibility that you could win. Why wait for the inevitable though? Better to just "rack em up" and try again in my opinion. :)