I have a question regarding atmospheric pressure. I understand that if a tank of water is open to the atmosphere, atmospheric pressure is mediated throughout the entire liquid because it pushes onto the surface of the liquid.

On another hand, say we got a pipe, and that pipe has a certain pressure within. Say then we drill a hole, and put in a piezometer to measure that pressure. Now, that piezometer is open to the surface, and the liquid in the pipe is essentially in contact with the atmosphere through the piezometer. Now, wouldn't mean that now the atmospheric pressure has "access" to the pipe's contents, and is thus effectively increasing the pressure by pressing on the liquid through the small piezometer opening? I assume that the pressure on a planet without atmosphere in the enclosed pipe would be the same, and if we drilled a hole and put a piezometer in, the water would shoot up higher, and the difference in water would account for the lack of atmospheric pressure. But my question remains. Wouldn't pressure press onto the contents of the pipe through the added open hole of the piezometer, thus increasing the pressure, and changing the pressure reading, than what would originally be?