In the sand filter, a slow flow of water below an obstruction in the sand means that the weight of water pulls harder and that dissolved air has a better chance to escape. This air makes the obstruction to flow worse. The head is negative with respect to gauge or atmospheric pressure. The soda straw analogy causes some problems because it is static. It is easy to appreciate that the pressure is lower at the top of the straw. The flow situation with the obstruction becomes more clear when you think of flow rates. The unobstructed flow is more rapid, and pressure drop is proportional to flow rate. The obstructed flow is less while the porous medium under the obstruction is the same. Less pressure drop because of lower flow rate means that the region under the obstruction has less pressure because the pressures are more or less equal further down the bed where the streamlines come together.
Somewhat similar is the concept of a "barometric leg" where a long pipe from a sealed tank of water dips into a tank of water at a lower depth. Water will flow through the pipe until the atmospheric pressure in the open tank balances the pressure due to weight of the water in the higher tank plus the height of the connecting pipe. This makes the upper tank at a pressure below atmospheric.