No, sorry, but this is a fractally wrong statement to make.
What do you mean by "fractally wrong"?
With sufficient curiousity, you will be dedicated to learning as much as you can. The drive to learn will push you where you need to go. Intelligence merely sets the speed by which you'll arrive.
True, but I'd argue that "mere" speed is pretty important. There are only so many hours in the day. A particular problem with modern science--bad enough in Einstein's day, worse now--is that there's a whole lot you have to learn before you can hope to make meaningful new contributions to any field. To refer back to an earlier famous scientist, standing on the shoulders of giants is great, but a lot of times you reach the shoulder of the giant only to realize that you're staring at the feet of the next giant. The climb will take you a long time even if you're very smart; if you're not, it may well take more than a lifetime to complete. Having just finished a PhD that took [mumble mumble] more years to complete than I expected at the outset, I'm acutely aware of this problem ...
Your over-emphasis on intelligence is elitism; It's suggesting that if you can't be "smart enough", you shouldn't be in science.
Hardly. No one really knows at the outset if they've got what it takes, and everyone who wants to do so should certainly give it a try. Even if they don't reach the top, they'll learn a lot along the way. But not everyone will reach the top, just as (mixing metaphors a bit) a whole lot of people who set out to climb the world's highest mountains don't succeed, and often die trying.
Anyone can be a scientist. It is a method, a way of learning about the world.
In that sense, sure--anyone can, and everyone should. But that's not the same thing as "doing science" the way Einstein did, making major discoveries that change the way we look at the world. Hell, it's not even the same thing as publishing a few highly cited articles, which is a fair accomplishment for any working scientist to aim for.