The BBS method is based partially on studies were participants who worked out more often and for longer in the gym produced no noticeable gains more than the group that worked out using HIT once a week. The rest is both Dr. McGuff and John Little's personal experience, for McGuff, as a MD and both for owning a gym were they have seen results in their clients.
In several interviews, youtube, McGuff mentions a study were the traditional method of working out only netted an average of 3% increase in gains over HIT once a week. The risk of injury was greater in the 3 day workout and average time was nearly 3 hours compared to just over 20 minutes. So you have to ask yourself does the risk and time match the reward.
I do not recall in reading the book or watching his interviews were he ever states that you are wrong or ignorant if you follow a more traditional training. I believe he regularly mentions that you should do what works for you and only suggests attempting the BBS workout for a month to see if it works out for you and if it does not go back to doing what you are doing.
Also you need to understand that this exercise system is meant to increase your strength and improve you physical appearance. Not to become awesome at some sport/event. So if you want to be a bodybuilder or a powerlifter you should workout in a method that benefits that particular sport. I just want to be fitter and not spend several hours a week in the gym, and because I have seen great improvements using this method I will stick with it for the foreseeable future.
Muscles do not understand how they are being affected upon, your leg muscles can not tell the difference between a squat and a leg press. More than likely you can use more weight on a machine, since you do not really have to worry about falling over and crushing yourself, and we know that muscle has to be broken down first and more weight is better at doing it. So from this standpoint machines are better. However free weights have their place obviously if you plan on partaking in competitions they will be using free weights and you do learn balance as well. But the key point here is that your body can not tell the difference between 200lbs on a bench press from 200lbs on a chest press machine, and so will respond to both in the same way, ideally by building more muscle in the chest and tris to allow a greater weight to be lifted.
As for the Nautilus comment, yes their machines are better but you will only find specialized gyms like the two authors have that are fully equipped with those machines. Every commercial gym will get the cheapest machines which Nautilus and MedX are not. That is not to mean you have to use those machines. My local gym has life fitness and Hammer Strength machines. I have seen gains on them maybe not as much if I had access to Nautilus machines but you have to use what you got.
Everyone needs to understand that what is important is that you fully fatigued your muscles. The method of doing so is less important, to the point of irrelevance in some cases. If you work out using a more traditional method and you workout hard and show gains then good on you. If you use the BBS or another HIT method and show gains then good on you. You do not really gain anything to argue that one method is better than another because as soon as some one says they have made gains your argument is invalidated. All study participants have always made gains irregardless of what method they used, so the takeaway should be to use what works for you and you enjoy doing enough that you do not loathe going to the gym.