They have the power to hold the market down to buy up cheaply, then they push the market up, which in turn pushes up the Alt Coins.

By controlling the dollars, they control sentiment. If the market is moving up, people want to get on it, which further pushes the market up. Once it reaches a point, these big players take their profits, and the market recedes extremely quickly, and everyone exits their trades at a loss to get out of a falling market.