It's sort of like this: In 2010 we had 3 top tier aces in Lincecum, Cain, and Bumgarner and we steam rolled our way to a world series championship while everyone's bats mysteriously fell asleep against the Giants. I think that was a title in just about every postseason series that year (Braves bats fall asleep against Giants, Phillies forget how to hit against Giants, top offensive team of the year Texas Ranger's bats go cold against Giants... mysteriously of course). Media outside of SF only recognized Lincecum and considered Cain an average #2 guy despite the 2.5 era through most of the year, I guess because of lack of wins with low run support. They wouldn't even mention Bumgarner despite a nearly sub 3 era in his rookie year and 8 shut out innings against the Rangers in the WS.
Then in 2012 Lincecum was having some major issues with his command, and really his health. So Cain and Bumgarner (and Vogelsong who came out of nowhere with a sub 3 era) led the Giants to a championship, which was a bit harder missing a Cy Young winner, but Cain and Bumgarner ultimately were top aces, Vogelsong was having an ace level year, and the Giants swept them as well.
Then in 2014 Giants had definitely gained in offense compared to past years but Lincecum was still having some real problems with his health and command and wasn't starting material. Cain was also hurt and couldn't pitch for us, and Vogelsong had lost some of his command and speed due to age I'm guessing. The one ace we had left of the big three was Bumgarner and he took over and won it for us like you said. But it's not like we got him at free agency or something. He had been a huge ace for us since he was drafted as our #3 ace, then our #2 when Lincecum went down, and finally #1 when Cain got hurt. Our team was built around those guys, they were the bedrock of the Giants championships. It's not that Giants fans were lucky Bumgarner was on our team, it was lucky the Giants could do so much without their other primetime ace Cain! We built our teams around those 3 and when two of them weren't able to be the starters they somehow managed to muddle through and beat a good Royals team. I have a lot of respect for the Royals of 2014, they had disciplined at bats, rarely struck out, played great defense, had some good starting pitching and the best bullpen in the majors. But if Lincecum, Cain, and Bumgarner had all been pitching without injuries it wouldn't have been close, though I don't think they would have been swept like the Tigers and Rangers.