I'd say so too! Maybe its just the way its written, but if the problem stops when the water to the kitchen's turned off, that's where the problem is.
Never heard of rats eating water pipes. More likely two-legged rats didn't glue the pipes carefully.
I had exactly the same problem and had to break some concret to isolate the leak. Water was just draining into the ground - no visible damp patches. Pure luck finding it. Good luck.