Your 'no man is an island' argument is one made by many and is extremely faulty.
Arguing against interdependency while you post on an internet built, maintained, and made possible by the largest collaborative human effort in history is incredibly ironic.
Past that, the rest of your argument is a strawman. Of course people have to work hard to succeed. What is missed entirely by those that support the Objectivist view point is that while success is dependent on your own work ethic, the level of success you can obtain is dependent on the world around you.
For example: Take the original crop of NASA Astronauts. If you've never met one, they are impressive folks. Many hold multiple advanced science and engineering degrees and even at their advanced age, many are in better physical shape than the average American.
Put an Astronaut on a deserted island. They'll do pretty well for themselves. They're smart, resiliant, in peak physical shape, and pretty crafty. But will the Astronaut ever get into space on their own?
The answer is no. Something like the space program is dependent on the hard work and engineering know how of a large group of individuals. Its financed and put together by an enormuous public effort.
The same argument applies to the theoretical Titans. Without the existing educational know how, Civil Rights structure, market apparatus, and yes, workers, they're just people. They're Titans because they work hard and enjoy the support and success that is possible because of the society they live in. In Rand's story they're not heroes. They abandon their life work, the loyal employees that toiled for them, and society as a whole because they felt cheated of their success... in short they duck the responsibilities to the society that helped make their success possible.
Coming full circle, that's why the quote:
Kung Fu Monkey said:
'There are two novels that can change a bookish fourteen-year olds life: The Lord of the Rings and Atlas Shrugged. One is a childish fantasy that often engenders a lifelong obsession with its unbelievable heroes, leading to an emotionally stunted, socially crippled adulthood, unable to deal with the real world. The other, of course, involves orcs.
Is actually quite appropriate. The "I don't need anyone" argument is something that a rebelling teenager says to his parent. It is an immature argument that one should outgrow.