those insiders could be choosing an action that affects the markets, or thru inaction, affect the markets.
The current insider trading rules only prohibit actions, and does not prevent inaction.
As an example, you could imagine that an insider were going to sell their portfolio of company issued shares, but because of insider info they have about a current project that would give rise to a price hike, they may choose to sell _later_ (or not to sell at all). This means the liquidity of the market is now less, and thus, raises the price vs the counterfactual world where said insider _did_ sell. All without revealing any information about the actual insider project.
but doesnt the central limit theorem require each event to be i.i.d. ?
I dont think the efficient market is a result of the central limit theorem, since each transaction affecting the market is not independent of each other.
