So my 2007 BMW e90 320i Auto randomly started with an issue where the brake pedal is really stiff and difficult to press, therefore braking is slow.

I did some research over 48 hours and thought it could be the brake booster so I did the tests Iv found online and been advised by some. The brake pedal remains in the same position, at no point does it soften, or go down a little further.

Decided to go to the local brake specialist, they jacked my car up and took a look. They advised the reason is my brake pads need replacement as well as my discs require skimming (front and rear) I pressed them on this and asked if they were sure, I raised my concern over the brake booster and vacuum, they assured me its not that and further explained how its caused by the pads and discs.

So my concern is, because of my previous assumption it was the brake booster - I feel maybe these brake specialists are mistaken or perhaps not sure. As I have not found anything online that leads in that direction.

So I want to know, can faulty/damaged brake pads and discs cause the stiff/hard to press pedal reaction? Could the skimming and new pads with sensors resolve this issue?