If I remember right, the way it was explained was that a ninja could very well have the skills necessary to learn jutsus of any nature (just look at guys like Kakashi, Jiraiya, and Hiruzen for this). Though it may be rare, it's possible. The nature affinity thing is just what a ninja is born with - such as, say, Naruto is towards Wind - making that element easier for them to learn compared to others. However, if Naruto focused enough and trains harder, he could learn Water, Earth, Fire, or Lightning... but his personality type doesn't really match many of those (perhaps Water would be the closest thing).
My big question is.. how is a character determined to have a sort of nature? For example, a character could be more fit to battle strategically with Earth-based jutsu (or in taijutsu, remains very defensive) while at the same time has a fire-like personality but born as a Libra. Which of those traits go into determining their affinity?