This question is and will always be debated. As a smart person would tell you, it depends. The style of training determines how this question is answered. Typical weight training consists of rest periods which are taken after each set is completed. Although this type of training gives the muscles adequate time to recover between sets, it does not keep the heart rate elevated or the body in an aerobic state. However, if the right activities are performed between sets in place of the rest periods this can quickly transform a standard weight training program into a hybrid cardio and strength training routine. These activities could be anything including: another strength training set, a core exercise, or a plyometric circuit.
Another huge factor which should be taken into consideration is the duration of each exercise. Standard strength training activities are generally measured by sets and reps. In contrast, the alternate activity can also be measured by time. When first implementing this type of program, a good rule of thumb is to use one minute intervals. This is enough time for the isolated muscle to rest and recover from the strength training exercise while still keeping the heart rate up.
In addition, the number of reps in each strenght training set should also be taken into consideration. Heavier weight and lower repetitions generally requires more resting time in between sets to let the body recover as much as possible to be able to withstand such force again. Therefore, the time to recover should be increased to three or four minutes. In this case, the individual should spend more time doing this alternate exercise/s to keep the heart rate elevated and use more oxygen as a source of energy. The individual must understand that because the muscle is not spending as much time under tension as a typical 12 rep set, one needs to push themselves harder to achieve this level. Remember that the goal of making strenght training cardio is staying really busy at all times.
Similarily, if the individual is training with high volume sets, then the muscle is spending more time under tension and the body as a whole is working for a longer period of time. As mentioned earlier, a one or two minture break is enough time to recover the muscle, elevate heart rate levels and engage the cardiovascular system.
Bottom line, weight training can also be cardio if the heart rate is kept elevated. Replacing rest periods with other exercises in between sets, adjusting the number of repetitions and amount of weight in each set, and using time to manipulate the routine will accelerate your heart rate, burn more fat, and give your body the same benefits of doing cardio all while building muscle at the same time. We all have preferences, but I suggest each one of you give this style of training a shot and determine if weight training as cardio works.