Your theory is absolutely correct. Why? Because "fast twitch" guys are guys with higher FRCs (anaerobic capacity). This capacity is a finite, clear amount; e.g. it might be 24kJ or 18kJ, etc. How fast you can run a given distance is a combination of your aerobic capacity to power generation (threshold) + whatever you get from FRC. A fast twitch guy is one with a very large FRC, and because that FRC is so large, it is a huge percentage of power they can generate at short distances.
If you can generate 300w aerobically, but have an FRC of 30kJ, then you can do 800w for 1' or 400w for 5'. By the time you get out to 30' though you can only do 317w.
Contrast this to a slow twitch guy with a threshold of 330w (faster half marathon by around 10%, so this might be like the comparision between an aerobic 800 guy and a 10k guy) but a modest FRC of just 15kJ. This guy can do 580w for 1', 380w for 5', but at 30' can do almost 340w, vastly beyond what an 800 guy could do.