Siphoning is due to the difference in weight of the water columns of the "U" shaped tube.
Siphon works on the basis of the difference in pressure. A portion of air inside the bottle moves out when the bottle is pressed and released. The pressure inside the bottle thus decreases. This pressure difference makes water to flow from the high-pressure to the low-pressure region. Therefore the atmospheric pressure will push the water up and thus flows through the bottle as shown below.
Therefore, the given statement is false.