How do people manage to get carried to diamond?

Almost impossible.

However, you can hedge your bets by both mastering being a participator in all fights, while also giving up very minimalistically little, even if you're a bad player.

Maintain 6-8 cs/minute Die less than 3 times per game Participate

Even if you're poor at calculating capacity to kill or angles, etc, Doing the above three things will result in the ability to climb to "close" to diamond just mooching teammates. The reason this works: You basically make the opponent's game reflect playing a 4v5 in respects to winnings and takedowns, while you still more or less have 5v5 Offensively.