Hello walter: We sort of agree, or at least the disagreement is not enough to fight over.
Seriously though, here is some background from photography. Apologies if you already know this.
For photographic lenses, the DOF is a function of the image magnification and the aperture and nothing else. The aperture is represented by the F number i.e. the focal length divided by the stopped down objective aperture. Thus stopping a lens down to F16 from F4 increases the DOF. Less obviously, reducing the subject distance - i.e. focussing close - reduces the DOF. Thus for real close up the DOF is small.
Assuming that this simple analysis applies to binoculars, and ignoring the effect of the human eye, we can see that two 8x30 binoculars will have the same DOF, and an 8x40 one will have less DOF due to the larger aperture. However in practice the human eye acts as an aperture stop. In good light the human pupil dilates to about 2mm, and so as far as the observer is concerned both the 8x30 and 8x40 binoculars will be acting as 8x16 binoculars, and will thus have the same DOF!
However ... some years ago I had a Nikon 8x42 HG, bought used, and a dealer pointed out to me that it was out of collimation. Goodness knows how I missed that (maybe knocked in transit to the dealer?), but on checking, the right hand optical assembly had noticeably less DOF than the right hand one. So clearly the DOF is also influenced by optical alignment. I also wonder if it is affected by optical quality? (In a sense this overlaps with optical alignment, except that instead of an element being out of position, one of the surfaces is a bit too steep, or not steep enough.)
Lastly, if we consider two 8x30 binoculars, one with 95% transmission, and the other with 70% transmission, then we might expect that the observers pupil would dilate more when using the poorer quality instrument, in order to compensate for the lower light transmission. Thus the perceived DOF would be less due to the larger effective aperture. I wonder if this partially explains the observed differences in DOF?
Leif