I think you have this backwards. I have always read that weight training spikes your metabolism for a longer period of time after a workout then a session of cardio. So the after effect of weight traning ends up meaning faster fat loss. On top of this if you weight train and add more lean mass you burn more calories.
I have always read and known that "moderate" cardio (those on drugs can increase this to extreme) plus weight training is best for losing fat, but if you have to only choose one it should be weight traning along with a good diet. This holds true based on you burn more calories for a longer period of time following the workout, and the gain in lean mass ultimately leads to more daily calories burned. As a side note weight training can give the effect of cardio by keeping the heart rate up by limiting rest intervals to 30-45 seconds. I don't know about you, but after a hard set my heart is puming, and I don't wait until it drops to normal to do another set.
No, it's correct. Cardio, particularly high intensity cardio, causes a greater after burn than weight training does (At least what most people I see in the gym do, which is: do set, chat, sit on their butt, do another set, go to the water fountain, etc.).
The increase in calorie burning after exercise is related to both the degree of elevation of the heart during activity, and the amount of time the heart rate stays elevated.
But you are 100% correct in suggesting that some forms of weight training (such as supersets) which keep the heart rate elevated above 60-70%MHR are essentially cardiovascular workouts.
So if you are taking very short rest periods (45 seconds would be a little long IMO) then you technically are doing cardio.
And seriously, cardio is essential for maintaining a healthy heart and cardiorespiratory system. I think it's foolish not to do any cardio at all (and by cardio I mean any activity that sustains an elevated heart rate, so that would include some types of weight training).
Anyway, you can get as buff and muscular as you want, but if you do not maintain good cardiopulmonary fitness you are not fit. I've seen a lot of bodybuilders who look great but who can't run a block and have elevated triglycerides and hardened coronary arteries and other health problems.
Carrying a lot of extra skeletal muscle on one's frame increases the necessary cardiac output, thus straining the heart and potentially causing cardiomegaly and other serious healthy problems.
If you build extra muscle it is even more critical that you maintain a healthy cardiovascular system, and some aerobic activity is absolutely essential to doing that.
PS I highly doubt that any reputable source would recommend skipping cardio altogether. That's just irresponsible from a health standpoint.