The "old husband's tale" was once valid, but is not any longer. Not
that many years back, the standard container for lead-acid batteries
was hard rubber. It was a good insulator and resistant to acid, and had
the benefit of some resilience so the cases didn't crack or split at
the seams. You might, with some luck, find an "antique" hiding in
someone's garage and be able to inspect the casing of one of these
beauties yourself, though most of yesterday's batteries have long since
been recycled at the local lead smelter.

The danger of concrete was not electrical in nature but rather
chemical. Lime (calcium) in concrete or cement could pass through the
hard rubber compound whereas the acid could not. Cold wet concrete, not
unusual for a garage or driveway, set up the conditions for the lime to
actually leach into the battery casing, and it would, aided (I think)
by the charged ions of the electrolyte egging it on. Battery activity
requires a certain concentration of the acid, measured by its specific
gravity. The lime would neutralize some of the acid, altering its
concentration and producing a salt which would pollute the plates of
the battery. The electrolyte would have to be purged and the salts
washed out before you could put fresh acid of the proper concentration
in-- just a pain. Further, because the lime got permanently into the
rubber itself, it was less resilient on the bottom of the battery and
was more susceptible to the same pollution at a later date. Hence the
battery manufacturers would warn the service-station and garage owners
to always rack their batteries and not store them on the floor once
they had been "filled".

The military were the first to use acrylic and pvc cases for their
batteries, which were often filled and ready for use many months prior
to their actual use. When good strong pvc cases were economically
feasible in the mid '50's (think Tupperware), the battery industry
moved quickly away from rubber and into plastics. It was a good move,
being at once cheaper and solving the lime-leach problem. The cases are
also lighter and don't tend to expand or contract as much, important
because the seal between the case and the terminal posts, which used to
be a real bugaboo, is now truly tight. And the plastics transfer heat
to the outside of the battery better (though now, with today's tight
engine compartments, a battery over-jacket of foam rubber is sometimes
needed to protect the battery from the heat of the engine!).

How long would it take for a rubber-cased battery's electrolyte balance
to be upset (to the point where the battery's life was significantly
affected) by lime leaching in? I have no direct experience, but would
guess that a couple of months would be enough. But long before that,
you would probably be able to measure a voltage drop in the cells, due
to a less effective concentration of electrolyte-- possibly after a
week or two. In the battery biz, where you have to take ambient room
temp into account when measuring a cell's specific gravity, where .5v
differential between (nom.2.2v) cells can be a cause for concern about
the battery's health, little things can cause a big spoil.

Some of you old-timers in the telcom industry will probably remember
glass jar casings for some of your huge central office batteries. They
were taking no chances back then...