VERY false. Just like any talent, some have it and some don't. Sure there are fundamentals to every art form, just like singing or playing an instrument, and if you learn them you can work at being better. But to be really good at photography, you've gotta have the "eye."
80% or more of what makes a beautiful photograph is the composition. (2/3 - 1/3 balance of color, value, shape, etc.) Some people have an impeccable eye for composition, and can take an exceptional photo of almost anything. Some people have a fantastic eye for subject matter too. Not everyone can make an inanimate object say something.
ALSO, when it comes to photographing people, just like with painting, getting a likeness of the subject is very VERY hard to do. Some people behind a camera (my grandmother for instance) can make even the most beautiful person look hideous. I've found, however, that the way a photographer captures an emotion behind the subjects eyes is what makes them really great.
So basically, it's a big fat lie that "anyone" can be a photographer. If that were true, everyone might as well pick up a cello too, because if we practice enough we'll all be Yo-Yo Ma.