Most speed reading courses are based on theories as solid as air. Peripheral vision does matter in comprehension, but that doesn't make them suited for the bulk of information processing, let alone rely on them. When you actually take in information from the periphery you usually piece it together from imperfect cues, which suffices for waffly material but won't work if you're reading a textbook. Duh, you say, but the amazing courses will tell you it works for everything, and people believe it!

The read-between-the-line thing, AFAIK, is just supposed to make your eyes backtrack less, which lessens fixations. More fixations = slower reading; it doesn't matter where you place your eyes.