Because the camera has a very small sensor (relative to full-frame) and thus a very large depth of field.
A 1/2.3" sensor is 6.17mm×4.55mm, giving a crop factor of 5.64 to full frame. With this, we can plug some numbers into any of the numerous hyperfocal distance calculators on the web (I used this one but it doesn't really matter):
- Sensor size: custom
- Sensor width: 6.17mm
- Sensor height: 4.55mm
- Lens focal length: 4.25mm (calculated as the 24mm equivalent divided by the crop factor, 5.64)
gives us a hyperfocal distance of 1.25m, and a hyperfocal near limit of 0.63m - i.e. if focused at 1.25m, everything from 0.63m to infinity will be in "acceptable" focus. That they come up with 0.5m is just because they have a slightly different definition of "acceptable", but in any case it's not far off.