Yes. Both are true. It depends on the type of game you want to play. D&D has been able to be played both ways since it's creation. Though mechanically, different editions have made this easier than others, and all have been mechanically weighted away from the ordianry hero style.
I'm certianly hoping that 5E is designed in a way that both can be supported equally...which is really the point of this whole, long, circular discussion.
However, I think your characterisation of the differences between the two styles is a little misleading. Sure, in the ordinary hero style, it is true that anyone can kill the big bad monsters. The difference is that the hero's actually have the audacity or insanity to try...while the rest of the ordianary people, and the town guard, do not.