I asked my husband about this and he suggested I write the following
Do you have a link for this?
The concentration of sulfuric acid normally found in car batteries is 40% SA to 60% water. in these concentrations sulfuric acid is usually stored in plastic containers, note batteries are made of plastic. However, not all plastics are the same.
Strong concentrations of SA will decompose some grades of plastics, particularly those with high organic or volatile component.
All of this said, there is probably a better chemist in the house than he is. He did though, suggest the decomposition of the rope in the above scenario would more likely to of been caused by a combination of heat (from the engine?) and the sulfur dioxide emitted from the battery whilst being charged. In extreme circumstances this would be far more corrosive than the sulfuric acid.
I suggested we chop up bits of rope and experiment. He said 'no'
Not sure what exactly your chemistry question is, but the story about the rope breaking was reported first-hand either here or on Supertopo. Analysis of the rope showed traces of acid, but it could not be determined how it happened.
Batteries should not emit significant quantities of either sulfuric acid or sulfur dioxide in normal use, else we would all have a corroded hole on our car hood (when liquid level is low, you add only water, not acid), but it can easily be spilled during removal etc, especially in older style batteries.
The chemistry term, "strong acid" does not refer to concentration, it describes the ability of an acid to dissociate, even dilute sulfuric acid will damage nylon.
What is so scary about this is that if exposed to sulfuric acid, nylon ropes or slings may have no visible damage.
Out of curiosity, I once poured full-strength acid from an old leaky battery onto a light colored nylon sling, just so I could clearly see what acid damage would look like. All it did was give the nylon a very slight brown tinge. Comparable to a dirty spot on it. Spooky, for sure.