I can't find any reliable information about this. I don't have the full specification of the SD/MMC Card hardware.

Is it true? My high-level application doesn't need to be concerned with wear leveling when working with these cards?

EDIT

Could someone confirm that wear leveling is guaranteed by the SD specification? I want to be sure, because it looks like most vendors do it, but it is not required by the specification.

I work for a company that used to be a member of the SD association, we are familiar with the 2.0 (SDHC) spec.  The SD card spec has NO entry for wear leveling.  That is completely dependent on the SD manufacturer to handle that if they so choose.  We have seen that some likely do, while others very much do not (beware the super cheap knock-off SD cards).  SDXC may have changed that to include wear leveling, but I am unsure of that.  Unfortunately the only way to really show that is to get your hands on the official spec.  You can find it online most likely, but the SD association really wants you to pay for it.

As a side note, taking a 2GB card and writing it beginning to end over and over again averages about 10TB before the card is dead and no longer is writable.  Also, SD cards will not let you know when data is bad, i.e. wont return an I/O error like a PC harddrive will.  This might not be an issue for embedded designs as 10TB is a LOT of data, but it could be a factor for someone.
