I've been in more upset victories than I can count. It pains me to lose because of a 20 minute surrender just because 4 people really think having less kills than the other team is GG. I'm not convinced I deserve that loss on my record, and neither should you.
Typically, I won't agree to a surrender unless the enemy is handily crushing our base and consistently winning team fights. There's too much faith in "first blood wins the game," or "one fed champion wins the game." There is such a thing as overconfidence, which is quite often a deciding factor in many games. I've seen teams push us hard, get baron, zerg into the base for the win and fall over dead 0 for 5, and then our team immediately pushes back and takes out towers all the way to nexus before they all respawn, and then we eventually win - and I've seen it more than once. There is also such a thing as UNDERconfidence, and if you're willing to surrender at 20 for silly reasons, you probably lost the game because you yourself brought the weakness to your team.