The Best Training Frequency for Fat Loss

Does it necessarily follow that a six-day program will mean greater likelihood of illness and injury? Perhaps I read this wrong, but it seemed that the likelihood of overuse injury was found in the study of women doing repeated consecutive days of RESISTANCE training each week and not a combination of resistance and interval training (I am assuming an alternating schedule and no consecutive days of either). Six days a week is alot of training for anyone, especially when high intensity interval training is included, but when training w/ moderate intervals on 3 non-consecutive days and resistance training on 3 non-consecutive days, I wonder if the outcome would be the same as for 5 consecutive days of resistance training. Not to mention that it is a given that one should rest muscle groups trained under resistance for at least a day between workouts. The study mentioned had the participants hitting the same resistance exercises for the same muscle groups on multiple consecutive days.