Wrong, idorba... 'Battery Acid', AKA dilute sulfuric acid DOES indeed cause destruction to wood fibers, paper, cotton fibers (you should see my collection of 'battery acid' modified jeans), etc...!
After time, that dark spot near the battery in the photo above will just erode away, similar to water damage wood rot, but probably quicker depending on the moisture in the environment...
A neutralizing solution of baking soda & water (or battery cleaner spray) may help slow down the wood destruction - maybe an 1/8" sheet of aluminum over of the effected area would help as well...
Why anyone would place a battery in that manner without at least a plastic case to collect any spilled fluids, is beyond me...! Think about a cheap $10 item that can reduce or prevent expensive floor damage in the future...
Also, those messy terminal connections in the photo should, of course, be avoided at all cost... One of those cable terminal connectors appear to be the kind that clamps the bare cable wires with a small plated steel strap and two 1/4" steel bolts through the lead terminal...
In our battery shop, we call these 'Emergency' terminals - used only to get you home if your have terminal failure on the road... Repair or replace the cable when you get back home and put that 'Emergency' terminal back in the tool box - those terminals ALWAYS begin to corrode within months of installation due to their dissimilar metals construction - Lead, Steel, Zinc plating, etc...
Happy trails...