Saying that, the definition of genius in the manga =/= the real life definition(s). As others have pointed out, Kishi made it a point to show that Naruto isn't a genius.
Also, in the context of the manga, the whole "genius of hard work" is both a paradox and an oxymoron. While it is true that geniuses certainly work hard, the act of working hard does not denote a genius. Kakashi was shocked by Lee because it seemed impossible, but Lee worked impossibly hard, so much so in fact, that even when unconscious his body moved on it's own off of muscle memory. That has nothing to do with genius, but is a bi-product of him nearly killing himself working so hard.
I guess i'd put itachi as a genius candidate. Reasons: Mastery of sharingan, level of intelligence , level of power that surprisingly enough was able to match up to other badasses ie jiraiya, orochimaru, obito (yes i put obito because it was said in the manga by obito himself that if he didn't keep a few secrets from itachi he would be dead) and of course befcause itachi is just..well...COOL ^__^
Everyone else's genius is like a pro athlete.
3 days to learn the first stage (popping the balloon filled with water)
3 weeks to finish the second stage (exploding the rubber ball)
7 days to complete the Rasengan (putting the first two stages together)
This is due to 2 things.
1/ He has an out of conventional method for approaching difficult situations and problems - such as his clone sage chakra transfer, or his clone rasengan (clone, clone...) This enables him to solve problems that others, even smart people such as Kakashi, would have difficulty with. His way of thinking also has helped him find strange and novel tactics to beat opponents who should, in theory, be far stronger or skilled, with far more experience than he has.
2/ It is true that he has an incredibly small number of techniques. However, he has progressed these techniques further than anyone else.
- Rasengan: He progressed further than Minato, Jiraiya or Kakashi
- Sage mode: Further than Jiraiya
- Tailed beast mode: Although I am open to the possibility that his progression over Bee is solely due to the Kyuubi's special chakra...
- Even Kagebunshin he has found ways to use that no one ever thought of doing so...
Sure, he does not have the book smarts, or conventional intelligence of other so called geniuses, but I believe that his ability to take anything that he does and perfect it/bring it to levels that no one else has ever reached before plus his ability to think out of the box and approach things in ways others couldn't possibly conceive of - sticks him firmly in the box marked genius.
Still doesn't make Naruto a genius though, it just makes him clever or more inventive. I mean, he had to find another way to make rasengan because he couldn't do it with one hand. A genius would be able to make rasengan with one hand, like Minato and Kakashi have. Naruto also has difficulty in understanding explanations, like when Kakashi explained elemental affinity to him. Nothing states that Naruto is a genius, in my opinion, just that he's clever and works hard.
geniuses are presented as people who pick up things way faster than their peers, people who can create new things, basically precocious guys who are good at everything.
Example, what Jiraiya needed 1 month to master Orochimaru mastered in 1 week.
Now, its also true though that the more time passes the more the hard-working guys close the gap and may end up surpassing the "geniuses", and that's because Kishi liked to show time and time again that those hard working guys are, in the end, people who are extremely good at something and that can reach the "geniuses" with enough hard work:
Rock Lee can go on way more than everyone else, and mastered 5 Gates at a young age.
Can Neji do that? No.
But can Rock Lee do 90% of the things Neji can do? Hell no.
Even better, let's use Jiraiya and Orochimaru for example.
Orochimaru was the genius of the two, but we see Jiraiya being probably the most complete ninja of the entire manga:
great strenght, great speed, great skills, great ninjutsu, great taijutsu, great genjutsu ( through Ma and Pa ), great stamina, enormous knowledge on Fuuinjutsu, Senjutsu user, incredibly knowledgeable and experienced, an accomplished writer and a great spy.
Orochimaru lacks Jiraiya's physical skills, genjutsu abilities but is actually immensely knowledgeable and a great ninjutsu/kinjutsu user.
But was the difference that thin at the beginning?
No, Orochimaru was miles beyond. It just took Jiraiya a lot of years to catch up, that's the difference imo between "geniuses" and "hardworking" types how Kishimoto presentes them at least, imo.
This is a prime example of why Naruto is not a genius, regardless of what people say or think. I think Naruto's smarter than Kishi shows or what he's given credit for, but a genius he is not. Orochimaru was known as a genius and was able to understand the purpose of the bell test before HIruzen even finished speaking. Minato was able to make rasengan (I don't understand how he copied bijuu bomb) from nothing, and he managed to create Hiraishin.
Naruto did complete rasengan and take it further, but it doesn't necessarily make him a genius. He most likely worked hard to do that, without fully understanding what he was doing.
Knowing that didn't require book smarts, Kakashi basically dumbed it up that anyone could understand. A genius in the first place would likely complete the sentence or be able to understand quickly.
How is it mean? Naruto's shown he didn't completely understand stuff, but it didn't stop him from trying it or training to do it. Though to be honest, I can't think of an example right now.