I agree that the message is a little confusing, because you have a group of guys in hockeypads in TDK who Batman says shouldn't be Batmen. Then he turns around and says that anyone could be Batman.
However, I get what it's ultimately trying to say.
Not everyone can be Batman. A group of men in hockeypads cannot be Batman.
However, anyone can be Batman. Any child who witnessed his parents murdered could be Batman. Anyone who develops the skill and acquires the resources or money could be Batman. Bruce Wayne is "anyone." He is special, and so is John Blake.
In other words, you can't just put on a Batman mask and "be" Batman. You have to be Batman before putting on the mask. That's why Bruce Wayne is special, and why Blake is special.
Another way to look at it would be like looking at a crowd of a thousand people. Out of that thousand people, not everyone could be Batman. However, anyone could be Batman. Bruce could be among that group of a thousand. John Blake could be in that group, etc.
If anything, the idea totally reinforces how special Bruce is. Not only could Batman be anybody, but Bruce actually did it. He actually was the person who went beyond the "could" and became something.