I think an elevated HR due to lifting heavy weights is different than that of running or other activities. An elevated HR response can be caused by a number of things outside of the "exercise your heart model" - if you will. Body positioning has a lot to do with heart rate responses. If you’re performing a set of leg presses, the position of the body - knees tucked into chest - will cause the heat rate to elevate. If you are performing presses flat on your back your heart rate will be lower than if you were pressing standing up- even if the relative intensity is the same. Holding a heavy weight causes an increase in blood pressure with leads to an increased heart rate - just by the nature of the activity. During times or excitement or great stress the heart rate is also elevated because of the release of various hormones - not related to exercising the heart.
I think that heart rate is very specific and is only on factor when determining the effect on improving the fitness of the CV system. The other is oxygen consumption. This is where the term VO2 max stems from - heart rate has always been used because it is easier to monitor in the field. O2 consumption is done in the labs. During traditional modes of CV activity - running-biking- etc. (all but swimming) - the heart rate is elevated in proportion to oxygen consumption - do to the need to transfer oxygen and nutrients to working muscles. So if your heart rate is raised to 150 BPM than Oxygen consumption would also be raised. However, if the HR is elevated because of a specific body position than the oxygen consumption might not be as high. Therefore causing no improvement in CV fitness.
There is no doubt that HIT raises both heart rate and respiration - breathing heavy. I just don't know if it is enough to improve ones fitness without additional CV training. - Doug Scott