There are two types of speed.
a)Finesse speed. This type of runner is a fast sprinter because they have good neuromuscular coordination, good muscle and tendon elasticity and an excellent, balanced running form. Sometimes with this type of runner you think they are not trying hard because they look so good running at full speed. Examples: Seb Coe, Wariner, Kipketer
b)Power speed. This type of runner is a fast sprinter because they have a muscular thighs and upper body which they use to power themselves down the track. These runners are often much heavier. Examples: Tyson Gay, Michael Johnson
So it all depends. Speed is very, very important, but it is not absolute. If take someone who looks like an NFL linebacker and powers out 11/24/55 for 100/200/400, of course will not break 30 minutes for 10k, even with high mileage.
If you get a skinny little 5"5'guy who has no upper body muscle and flows his way to 13/26/55, then he has a good chance that he could be a solid distance runner if he works at it.
Look at it this way. You are a 50/3:30/12:45 guy for 400/1500/5000. You want to work on your 400 speed for a year as you feel it is one of your weaknesses. You can go about this two ways-increase your power output or train your body to better use the power it already has. If you try the former, you will be in the gym, taking protien and bulking up, and this will not help your 1500 and certainly not your 5000.
But if you go about it from the other direction-with drills, hills, increasing muscle and tendon elasticity and improving your running form, you will not only avoid bulking up but your 1500 and 5000 will possibly IMPROVE because you become more effecient and cover the track more easily with the same power output.
All run approx within a second of 20 seconds/200m
Coe:
http://sdc.lboro.ac.uk/smallest_images/seb_coe.gif
Wariner:http://karlesmontalt.files.wordpress.com/2007/10/jeremy-wariner.jpg
vs
Tyson:http://www.iaaf.org/mm/photo/competitions/competition/gay_tysonmtsac_2210_full-prt.jpg
Johnson:
http://www.ontrack4gold.com/gallery/STAR-JOHNSON_Michael_19960801_5.jpg