I can tell you of two examples that I have personally gone through.
1) 9 years ago- I was 285lbs. I adopted a high protein, low fat, low sugar, low carb diet and did weight resistance training 4 days a week (I did the push pull method) I did not work my legs at all. But my job at the time was a Tower Climber- so essentially I was doing a stair climber type movement everyday.
other than that I did 0 , nada, zilch cardio. One day I jumped on my treadmill and I ran 4 miles at a 7 minute mile pace. So that is 4 miles in 28 minutes. I got bored running on the treadmill after 30 minutes and just stopped it. I felt super fresh and could have gone further but just was bored.
2)this time around (2007) I was a little over 300lbs- I again adopted weight training and low carb, high protein diet and lost 85lbs in 12 weeks- I incorporated distance running into my program and did not do any resistance training at all- I ate more carbs (because that is what runners do) and my best time for a 5K was 24 minutes (4 minutes slower than when I wasn't even running in example 1)
Now you could say- well you are 9 years older- you were not the same weight, etc.
But I do think to be able to run 4 miles in 28 minutes says alot for what weight resistance training can actually do for your cardio.
Well that is my $0.02 worth.