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Studies that claims "learning by teaching" has a 90% retention rate cites a study published by "National Training Laboratories, Behel, Maine". However, that study is not available anywhere to confirm if the methodology applied is reliable.

Example of the claim from Contemporary database topics: learning by teaching:

The Learning Pyramid shown in Fig.1b underpins this approach; it shows the effectiveness in promoting student retention of the material taught for a range of learning activities. Teaching others is shown to have the highest retention rate.

Image of Learning Pyramid

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Renan
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The answer to this question is going to depend on definitions - what is an "Average Retention Rate"? Based on how much teaching? etc. To understand the claim, we need to go back to the source.

But the source research behind this diagram has been lost in the past fifty years.

The research base for the pyramid is difficult to establish conclusively. It was developed and used by the National Teaching Laboratory Institute at their Bethel, Maine campus in the early nineteen sixties, when that organization was part of the National Education Association's Adult Educations Division. NTL believes it to be accurate but says that it can no longer trace the original research that supports the numbers.

The passage goes on to explain why, despite the discomfort in using data from a "tenuous research base" , they justify it to themselves as being appropriate for "a stimulus for reflection only". As a skeptic, you may take a differing opinion.

Oddthinking
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    I'd like to add that using the pyramid is bad academic practice IMO. Not only is it's source lost, but as Oddthinking points out, the graph is highly subjective to definitions (which I may or may not have been explained in the source) and is not self-explanatory, i.e. the underlying data and analysis can not be inferred from the graph alone. – MrLemon Jun 11 '14 at 17:06