Dangerous because someone could believe bad information, and trust me, trying to weed out the bad information is very difficult. Can't tell you the number of times someone has walked into the pro shop and said we were wrong because of what he/she read on the internet or from what someone else told them. We then have to spend time (which is ok) to show why the person is wrong and educate them with the correct information.
As for the OP question...I will take an extreme example. Take 2 Black Widows, same core, same company, and drill them identical. In your theory, because they have the same core and we drill the two balls identical, the ball will react the same/close to each other. However, after revealing that one is the Black Widow Spare with a plastic cover and the other has a traditional cover, the only difference is cover and I bet you will see tons of reaction difference.
So yes, covers drive ball reaction and the core allows you to fine tune that reaction.