I don't think I said it is necessary only to become fast. If one were to perform HIIT as I have described it on these forums using solely sprinting as an activity, the person would probably run into injury trouble. I actually do not recommend sprinting as an activity to anyone unless they really know how to and know that they can relatively safely - in most cases this means experience under a track coach. Sprinting well is a learned skill.
However, if one rotates through a variety of safer activities like stationary bicycles, calisthenics, jumping rope, etc... I think one can start at a moderately high intensity level and go up to a very high level fairly quickly and safely without needing any kind of work on an aerobic base unless one chooses to. The best protection against chronic injury is to pay rapt attention to proper exercise form and monitor any pain signals coming from the body - massage or minimal diagnostic self-massage is a great way to get early warnings, and start to re-evaluate your activities.