X-rays very much do travel through water. I think your quote may be out of context. For example, being deep in the ocean would protect against X-rays because there is so much water above you. However, concrete or lead are two more common materials which provide more protection against X-rays.
Using the link you provided, I generated the following plot of the transmission of X-rays through water. I used the formula H$_2$O and the density 1 gram/cubic centimeter:
"Atten Length (microns)" means that after one attenuation length, about 2/3 of the X-rays are absorbed. So after two attenuation lengths, only about 10% of the X-rays survive. If you look at the top of the graph, which is a photon energy of about 30,000 eV, this is still somewhat less than commonly used for medical X-rays. (For example, the most recent medical X-ray I saw was using 80,000 eV). At that distance, the attenuation length for 30,000 eV photons is about 30,000 microns, which is about 30 mm. Hence you need the better part of one meter of water to stop 90% of the photons from penetrating. At 80 keV, you may need more like a several meters.
[The algorithm used to generate the plot is described by: B.L. Henke, E.M. Gullikson, and J.C. Davis. X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92, Atomic Data and Nuclear Data Tables Vol. 54 (no.2), 181-342 (July 1993).]