While I have no idea as to the validity of the explanation, it does sound somewhat plasuible. The idea being if the battery is on a cool concrete floor, it will tend to enhance moisture buildup on/around the battery. The condensation (along with any dirt) will act as a high-resistance connection between terminals and slowly drain the battery. YMMV...
I believe that this is a very old urban (or automotive) legend. In garages, the area for charging batterys had a wooden pallet (most still do) to set the batterys on. I believe this was so you would not crack the hard rubber battery case that the cases used to be made from (easy to do if you dropped the battery on concrete). If you cracked the case on concrete and the electrolite leaked out, the battery would certainly discharge. The battery case was very much less likely to crack if dropped on a springy wooden platform.
The mechanism at work here is a microscopically thin layer of battery acid on the outside of the battery casing providing a path to ground for the battery current.
So, in theory, if you scrub your battery case clean, and maintain it clean, then there is no leak path, it will not discharge. Go ahead and set it on the concrete.
This explains why every battery set on concrete does not discharge. But, many have, so the phenomenon is real.
Now, before you pounce, this is what I was told by an engineer at an automotive battery manufacturing plant when I ask. I took his word for it, and am just passing it along. And, by the way, I am old school; I still set my batteries on a wooden block. I will set them on concrete for a few moments, but not for long term storage.
To fuel this question (which I find interesting) a friend of mine works at Ford dealership. He told me that vechicles parked in the showroom tend to have their batteries go dead... and they have to be frequently charged. I recall seeing vechicles at car dealerships in the showroom with chargers hooked up.
Showroom vehicles typically have their hoods up, or their doors open... and often the dealership will forget to remove the fuses or bulbs for the lights. That will drain a battery within a day. Other times, the cars just sit there for weeks or longer, never being turned over... even a simple car alarm and other accessories will slowly wear down the battery.
I am of the old school, very old ;-) school. I stored batteries on wooden pallets in the early 50's because I was told to do it that way. Old habits die hard. I still put a 'good' battery on the shelf as opposed to setting it on the floor. Like I said "old habits". That does not change the fact that with todays batteries it matters not one whoop where you store it---on the concrete floor, on a wooden pallet, indeed, hanging from the sky light---it will discharge at the same rate eventually going completely inert. There are several threads pertaining to this subject in the forums, some posts made several years ago, as I recall. Bottom line---at some point I did the "scientific"(there is humor in that statement) tests and found, by experiment, that the batteries go dead at the same rate, no matter where they are setting. (two identical batteries, deep cycle from my motor home, setting side by side, one on wood, one on concrete floor---checked weekly and after 3 months fully charged and positions reversed. Same results after an additional 3 months. Convinced me.)
That changes my habits as to storage of batteries? Nope, like I said "old school". You know, just in case my ideas are off in left field!
Oh, yes. I now only use "gel cell" technology batteries in most applications, race cars, motor home, etc.
The only way a battery can discharge is by some sort of electrical leakage path BETWEEN THE TERMINALS. I just cannot see how storing a single battery on concrete can make the slightest bit of difference.
Leakage to ground is not going to be an issue unless one battery terminal is directly grounded, or several batteries are connected in series. At the high voltage end, leakage to ground might then be a factor, especially if the final voltage is fairly high.
In large high voltage commercial battery installations it is preferable to completely isolate the dc system from ground, and monitor earth leakage current. This will usually bring up an alarm if it exceeds a few milliamperes. The biggest danger of earth leakage currents are usually from electrolytic action and corrosion. If the leakage is serious enough to cause significant battery discharge, the wiring is going to be eaten away very rapidly.
Traditionally, large battery racks are made from wood. It is strong, cheap, and resists battery acid.
I read a lengthy discussion of this topic once. All of the explanations here were mentioned and one additional that seemed the most reasonable to me: If the battery is sitting on a heat sink that creates a temperature differential in the battery volume (like concrete)a density gradient in the acid solution will occur. A small internal current will accompany the density gradient. So you need two things to discharge a battery: A big heat sink and significant temperature fluctuations.