according to DOF Master online, the LX3 should give about 6 cm total DOF, while the 5D should give about 30 cm total DOF, assuming focus is at 1m, and would be even less at a shorter focal point.
Sure looks like the LX3 has a little more DOF, doesn't it?
You are using the tool wrong.
Panasonic LX-3, 24mm (35mm equiv), f/2.8
24mm (35mm equiv) on LX-3 is 5.1mm actual focal length.
http://www.dpreview.com/reviews/panasonicdmclx3/
Lens • 2.5x zoom
• f=5.1-12.8mm (35mm Equiv.: 24-60mm)
So now input-
LX3 @ 5.1mm / f2.8 / 3ft subject distance
DOF = 5.5ft
Canon 5d @ 24mm / f2.8 / 3ft subject distance
DOF = 0.8ft
This lines up with what we see in the picture.
Now your statement can be both wrong or right depending on interpretation.
Facts
Effective focal length, on different sized sensors, has wildly different DOF.
Actual focal lengths, on different sized sensors, have same DOF.
Actual focal length
Put a 28mm summicron on an M8 and a 24mm on an M9, you get same DOF and the M8 looks cropped.
Now effective focal length
Put a 28mm summicron (28*1.33=37.24 effective focal length) on the M8 and a 35mm summicron on the M9. This will give you approximately the same angle of view. However, the DOF will be different. The M8 will look like the DOF of a 28mm, that has been cropped.
Note the sensor crop is small enough that the difference is 1.28ft 28-on-M8 vs 1.06ft 35-on-M9 for f2.0 @ 6ft.
But please understand how to use the tool before you go around shouting about its failure.