Unless there is a patent or Design Patent on the bullet shape, there is no patent infringement, so copying is OK. Lots of companies make stuff that looks like another company's stuff.
From the tests performed by Rank Amateur, the Hornady bullets do not group as well as the Bergers.
I believe that the difference is in the precision and quality control elements that Berger has perfected. Hornady will not be able to duplicate those procedures. A "State of mind" is established in the company that has a certain level of quality, and it is difficult to change that " state of mind". The people tend to make the product to that "remembered" quality level. Hornady has one level, and Berger has another level.
I spent 50 years in the manufacturing business, covering products from reactor rod drive controls on nuclear submarines, digital electronics, strain gage load cells, electromagnetic clutches and brakes, to AR500 Steel shooting targets. I would never have a person who ground slag on plasma cut AR500 targets work on assembling load cells in a clean room. The person's concepts of quality needed to match the performance characteristics of the product.
Yes, you can teach quality, but it takes time, and in general, there is a "corporate" quality level that permeates everything. I am not sure you can change that "corporate" mindset of quality. Hornady has a good quality level, but I believe Berger's is at a higher level.
Another factor is skill level. Learning the product, the process, and the machinery. Working longer at a specific process or product or machine will improve the skill level of the operator, and of the product. You need skilled people to make a high quality product. a bullet press operator has to be able to spot when to change dies, or to adjust the press to continue to produce winning bullets.
It is just like reloading for us, we start off following the manual, and our reloads shoot OK. With time and repetition, (and reading Accurate Shooter) we eventually start shooting X's.