No, this is a myth.
Car batteries do not usually corrode just sitting on concrete unless their is a leak in the container. I do know that you shouldn't place a car battery on a concrete surface as it can cause the battery to discharge its self into the concrete and you end up with a dead battery.
Rechargeable batteries have high self-discharge rates meaning you will need to recharge them after a few days of sitting or just charge them when needed.
they don't i have left batteries on concrete for months and had on loss of charge.
Leaving a battery sitting on a cement floor will have no effect whatsoever. It will not discharge the battery anymore than letting it sit in the car or on a wooden floor. That is a myth. Just put a charger on it and charge it. If it does not take a charge it is defective, but sitting on concrete did not cause it to go bad.
Mainly, I heard that it is harmful for the batteries if you allow them to discharge completely.
It actually is based upon temperature-----. Batteries are insulated in a plastic or rubber case, so electricity leaking to the cement is not in the question. Even more so, batteries normally sit in a metal tray in a car. If battery leakage were to occur, it surely would sitting on metal. The actual cause is temperature difference between the top of the battery and the bottom. The specific gravity of the electrolyte changes with temperature. Therefore the specific gravity of the electrolyte is less at the top of the cell and more at the bottom. As measuring the specific gravity tells the state of charge of the cell, the cell has more of a charge at the top of the cell than the bottom. This causes an internal current drain inside the plastic battery case. All batteries will discharge no matter where they are sitting when not being used. This is called "Shelf Life". A battery will not be damaged by sitting on a concrete floor versus sitting on wood. You will just have to charge it up to use it. It should be noted that a lead acid battery will eventually sulfate the longer it is discharged. Sulfation is not fully reversible. People who believe that a battery is ruined by sitting on a concrete floor don't realize that probably the battery was acting up to begin with and was removed from a vehicle because it was going bad. After sitting on a concrete floor for a period of time, they try to charge the battery and find it bad. Therefore the conclusion was that the concrete floor ruined the battery instead of the battery getting plain worn out from usage in a vehicle. It is all due to temperature and nothing else.
Cuz carpet is warm!
Their batteries could discharge deadly fumes.
They don't. That is just a myth. Modern batteries will not drain when placed on the floor even if it is concrete.
Yes. It is a myth that a battery will run down sitting on concrete.
Batteries can explode if overheated, or if they have been sitting unused for a very long time (i.e: in your old remotes).
lithium batteries have a faster current discharge rate then alkaline batteries but they cost more. The LIPO battery is used the most in RC planes.