Well, you can't have it both ways, Howie. If you agree that the perception of DoF on the print changes according to the viewer's perspective (distance from the print), then it seems rather illogical to maintain that changing the perspective of the camera does not change DoF.
Further to this interesting dilemma, there is a solution proposed by Charles Sydney Johnson in his recent article, Lens Equivalents. I quote the relevant passage below.
However, there is a caveat. The type of DoF computation depends on the way photographs will be viewed! In principle a photograph should always be viewed from its proper perspective point. That is to say, the angle subtended by the photograph at the eye should be the same as the field of view of the lens used to take the photograph. Therefore, photographs taken with a wide angle lens should be held close to the eye so as to fill much of the field of view while telephoto photographs should be held farther away. It is sometimes forgotten that perspective in a photograph depends only on the position of the lens relative to the subject (object).
So how will the photographs be viewed? In fact, prints are usually viewed from 10” to 12” regardless of the focal length of lens used to make the photograph. When mounted prints are viewed, observers typically stand about the same distance from all prints. Observers generally don’t know what focal length lens was used, and they simply react to the apparent distortions present when a wide angle photograph is viewed from a distance greater than the perspective point. Similarly there is an apparent flattening effect when telephoto photographs are viewed too close to the eye. Also, in photographic shows the audience remains seated at the same distance from all prints and from the projection screen. Under usual viewing conditions, it is appropriate to compute the DoF with a constant CoC in the image regardless of the focal length of the lens.
The first part of this quote, as I understand it, is basically saying if you use a wide angle lens from a closer distance, then, even though the resulting prints are the same size and the subject is the same size as in another print of the same subject taken with a longer focal length lens from a greater distance, the shot taken with the wider angle lens should be viewed from a closer distance in order to maintain the perception of equal DoF that is implied by the basic DoF formulas.
Let's flesh this out a bit with a concrete example. Let's take your example of 2 shots taken with a 50mm lens and a 100mm lens, the shot with the 50mm lens being taken from half the distance to the subject so that the subject is the same size on the sensor. Let's also assume that there is some significant background detail common to both shots, say a rather OoF house some distance behind the subject.
The fundamental DoF formulas are basically saying, in both shots the actual
resolution of the house is the same. If you were to enlarge the house in both images on your monitor, so both houses were the same size, you would see the same amount of detail in both houses. I know because I've tried it. (In case anyone is confused, we're using the same f stop with both lenses and have focussed on the same subject in front of the house.)
If we make equal size prints of both scenes and view both prints from the same distance, say the diagonal of the print so we can appreciate the fine detail of the subject, say Howard, then we will find that the house in the 50mm shot appears sharper. It appears sharper because it is smaller on the print. The DoF therefore appears greater in the 50mm shot.
If we move closer to the print of the 50mm shot, closer than its diagonal, the subject, Howard, will appear to be less
sharp and the more distant house will appear to be more
sharp. At some appropriately different viewing distance, both prints will appear to have the same DoF and we shall all be able to sleep soundly knowing that our mathematically based DoF formulas are accurate.