The shape of the pyramids was indeed influenced by the benben. Here's something I found on Egypt Tour:
One of their earliest creation myths envisioned the first place in the world as a mound of earth emerging from the waters of a universal ocean.[...]
It seems that the earliest temples of Egypt, particularly in the north, sometimes incorporated a mound of earth as a symbol of the original site of all life. The earliest such mounds may have been a small hill of earth or sand, but the icon eventually took the form of a small pyramid carved from a single block of stone, known as a bnbn (benben). This name comes from the root, bn, which means to "sell up" or "swell forth". The benben also, because of the sun's part in creation, came to be an icon of both the primeval mound as well as the sun which rose from it. In fact, the Egyptian word for the rising sun is wbn, which comes from the same root as benben.
The above extract tells how the "rising mound of earth" was imitated by the pyramids and how the Egyptians considered it sacred. That sacred feeling was achieved by the Egyptians through the construction of the pyramids.
Multiple sources do confirm that the Egyptian pyramids were based on their beliefs on benben:
First of all, they reflect the shape of the primordial mound of creation "benben". According to the Egyptian creation myth, which describes how the world was born, benben was an earthly mound that appeared out of the water and produced the first God.
source: Function of the Egyptian Pyramids
The pyramid was not only a recreation of the benben, but along with it, the pyramids were considered to be the steps to heaven, where at the peak, they (Pharaohs) could greet the Sun god, Ra.
Moreover, the origin of the monument, hitherto overlooked, made it a symbol of the highest sacredness, rising above the mortal remains of the king, to greet the Sun, whose offspring the Pharaoh was.
source: LECTURE III THE REALMS OF THE DEAD—THE PYRAMID TEXTS—THE ASCENT TO THE SKY
It is said that the myth is confirmed in the Pyramid Texts.