In answer to your second question, "How would a repair facility check for damage without pulling up carpet and opening up a wall?"...
1. Sight: Obvious wetness in the material, be it a wood surface or cloth/paper surface. As noted, it's the prolonged wetness that causes the damage, not simply the fact it's wet.
2. Sight: Bulges in the surface of either wood surfaces or cloth/paper-covered surfaces. The bulges are caused by separation and/or delamination of a wall/ceiling/floor's interior materials.
3. Sight: Discoloration of a surface, be it either a wood or cloth/paper-covered wall/ceiling/floor.
4. Feel: Softness when pressing on a surface where you would not expect the surface to be soft, such as a wood surface.
5. Feel: Rubbing your bare hand across the surface might reveal a texture change due to damage. For example, water damaged wood will usually become rough and grainy to the touch.
6. Sound: Lightly tapping or light knuckle tapping on a wall will reveal a possible damaged area by changes in tone to your ear.
7. Sight: Removing a metal screw at/on/over a suspected damaged area may reveal rusted threads or a severely damaged screw due to prolonged water presence.
8. Smell: Depending upon the material sustaining the damage, you might smell mold, mildew, etc.
Bottom line: If you do not want to pull up carpet or open a wall, then you have to use your senses (sight, feel, sound, smell) to make an educated guess as to the presence of damage.