I've heard all of that before. Some people say it's true and others don't.
I'm pretty sure all the miles I'm doing at the moment aren't making me faster but then I just want to get to 10k!
by reading that, this is how I see it (and I need to do?)
1) Speed Work - Do something like Hill Repeats or Interval training twice a week, or ride with a fast group
2) Long Steady Distance - Ride at a steady pace, not just "pedal" and try and get a good average speed, for example, the 20 miler I do I've been getting around 16 mph average speed and that's my steady pace
if I do 14-16 im not pushing enough
3) Variation - each week is different , so that I don't do say hill repeats on Monday, HIITS on Wednesdays etc.
4) Recovery - If I feel I need to recover, then do so, do a recovery ride but at low intensity or stay off the bike completely
5) Train off the bike - self explanatory really, GYM work Pilates or something