No, there is no truth to the statement that storing a battery on a concrete floor will damage/drain the battery. This used to be the case a long, long, long time ago when batteries were built differently than the batteries of today. So, go ahead and store your batteries on the concrete.
I, too, use the batteryminder as referenced by Bob (aka the Rustic Eagle) to maintain all my batteries. I would not recommend a battery charger found at Walmart, Farm&Fleet, or some other big box place. The key point is that you want to obtain a multi-stage charger (eg, batteryminder or battery tender) and not some basic trickle-charger (of which the latter is usually the type found in the big box joints).
Russell -- get a multi-stage battery charger; check the water level inside each cell before attaching the charger; attach the positive (red) clamp to the positive battery terminal; attach the negative (black) clamp to the negative terminal; then plug-in your charger. Check the water level every 6-8 weeks and add distilled water if necessary. And, yes, the batteries can be on the concrete and the charger higher, but not directly above, the batteries.
Finally, unless somebody has some data to prove otherwise, placing a battery charger higher than the battery should make no difference whatsoever to the battery; I do, however, agree with Bob that a charger should not be placed directly above the battery for the reason he stated.