The most likely causes are user input or a control issue rather than a normal camera fault.

First, make sure the camera is actually set to Single Drive mode. Don’t confuse this with One-Shot AF—that only affects autofocus behavior, not whether the camera can take multiple frames.

If Single Drive is selected, the 5D Mark III’s shutter button may simply be sensitive enough that you occasionally trigger it twice. The transition from half-press to full-press is light, and mirror/shutter movement can sometimes cause an unintended second press, especially if your finger stays on the button.

A good test is to see whether it happens less with mirror lockup or with extra care on shutter release.

Another possibility is a physical issue with the shutter button, such as dirt, moisture, or contamination causing intermittent double firing. If the problem becomes more frequent or repeatable, cleaning/inspection or service would be sensible.

So: verify Drive mode first, then consider accidental double-presses, and only suspect a hardware issue if it keeps happening.