"The entire pressure of the whole atmosphere is equivalent to about 10m of water."
This statement is utterly meaningless.

No, it is correct. Do you not understand?
The pressure of the atmosphere at the Earth's surface is equivalent to the pressure under 10m of water (or 76cms mercury.)

"We were told at school that one property of liquid water is that it is virtually incompressible."
Correct Steve.
At a constant temperature and pressure.

No Stu. Pressure has no effect on its volume.