One thing the MSF screws up IMO(and of the YCRS staff) is that they tell you not to cover your brake lever, I was riding before I went to MSF and always instinctually covered the front brake lever but when my instructor saw this she would tap my hand right hand but at the end of the class she said I was top of the class ?? Talk about mixed messages haha.
As someone else mentioned, if I were to ever feel that I couldn't control my motorcycle correctly I would not ride. Some confidence is needed or you will always be second guessing yourself and that is definitely not safe, move with authority and look where you are going. I personally never like to be near cars but here in NYC its unavoidable sometimes so when I'm splitting or have vehicles near me I try to keep an eye on the front wheels of the cars that can potentially come in my path. Another thing that has helped me greatly is going into a parking lot and stopping as fast as possible from 70mph to know how hard you can brake without throwing yourself over the bars, do it enough and it will be second nature a experienced rider SHOULD always outbrake a car.
They want you to keep an all round grasp of the bars in case your front tire hits something (pot hole, groove on the pavement, etc). If you have only a partial grip on the bars and hit something, the bars will get ripped out of your grasp and then real problems will occur.
You can scrub speed off by using the rear brake as well...in a panic stop, I use both brakes together.