Here are a few things to think about in terms of what we consider to be cardiovascular fitness.
First let's look at the way we traditionally assess the cardio system. Currently we utilize a stress test which requires that we endure increasing intensity of work via a treadmill until we reach our "stopping" point and then see how long it takes to recover, actively. This isn't the way we are told to train unless we are blessed to find someone that truly understands interval training. Typically we are told 30+ minutes a day and to "maintain" a percentage of your max heart rate. So the advised process of getting in shape doesn't necessarily coincide with the testing module.
Secondly, as we discussed earlier, one should get in shape to run, jog, etc first, not run to get in shape. If we aren't biomechanically sound from an orthopeadic standpoint, then we are creating another problem. This is largely why we have a massive amount of orthopeadic problems in our society. A large percentage of runners should not be running from an ortho standpoint.
Thirdly, in the USA, we stress cardio fitness above all else and it is what you see in our gyms, it's the first thing our MD's advise, and we've been told, it the most important system in the body. So why is it that we have the largest percent of cardiovascular and orthopeadic problems globally?
Training the neuromuscular system, trains the cardio system as well. Imprinting biomechanic efficiency and then taxing the neuromusc system will affect the cardio system in a way that requires that it, the cardio system, keep up with the work load and then quickly recover to get ready to do it again (sounds a little like the way we assess the cardio system doesn't it?).
I could keep going on this topic from both ends forever, but in the end it is my opinion that the most important system of the body is which ever one is the weakest. For it is through our weak point(s) that access is often obtained for our destruction.