He is correct even taking that into account. Quoting Bob Atkins:
"If you use the same lens on a Canon APS-C crop sensor camera and a 35mm full frame body, then shoot from different distances so that the view is the same, the Canon APS-C crop sensor camera image will have 1.6x MORE DOF then the full frame image."
A look at how sensor size affects depth of field. Why do digicams and crop sensor cameras have a greater depth of field thaan full frame 35mm cameras?
www.bobatkins.com
You can confirm by playing around with an online DoF calculator like this one, which takes the required circle of confusion for enlargement into account:
http://www.dofmaster.com/dofjs.html
However, you may end up forced to choose between more DoF or less diffraction.
You're applying what Bob said for one situation to what Fisher is saying for another scenario. When you crop, it's exactly the same thing as reducing the sensor size
without changing your shooting distance. If you backed up without changing the focal length you gained DoF at the expense of magnification. When you then crop without changing that distance or focal length to increase the magnification, you give the vast majority of that gain right back.
Try
Cambridge in Color's Flexible DoF calculator that allows you to press the 'show advanced' button and then enter all of the variables yourself instead of letting DOF Master assume them (often incorrectly) for you. Be sure to use macro shooting distances where the reproduction ratio will approach 1:1. That is, do not use subject distances longer than 4X the lens' nominal focal length.
Bob also says at the link you included:
"If you use the
same lens on a Canon APS-C crop sensor camera and a 35mm full frame body and
crop the full frame 35mm image to give the same view as the APS-C crop image, the depth of field is
IDENTICAL." (Which is a bit misleading. The total DoF will be identical, but the distribution of that total DoF between front and rear DoF will be slightly different.)
And while Bob acknowledges that at hyperfocal distances the difference in DoF between the 1.6X sensor and the FF sensor increases well beyond 1.6X, he neglects to observe that as we approach unity (1:1), the opposite happens. The portion of Bob's article that you quoted above is not correct at macro distances where the reproduction ratio begins to approach 1:1, just as he acknowledges it is not correct at distances where the rear DoF includes infinity.
Update: Actually, Bob does acknowledge it much further down in the article:
"Again, this simple analysis only applies at "intermediate" distances, but we have to have that limitation if we want a "simple" formula. It only really breaks down when the lens is focused further than about halfway to the hyperfocal distance or when we get to magnifications near 1:1"
A little bit further he also says:
"I'm sure some people will say, OK, but what if you don't take angle of view into account. What's the relative DOF if you use the SAME lens on a Canon APS-C crop sensor camera and a 35mm full frame body?"
"Now you run into the problem of what you are comparing to what. The same lens on the two formats will give you different fields of view, so if you enlarge each image to the same size (say 8x12), you won't have the same print so you really can't compare DOFs. If you crop the 35mm negative to give you the same print as the digital image the answer is easy. The DOF in the cropped 35mm print and digital image print will be exactly the same. You're using the same lens and same size image (cropped 35mm or digital), so you get exactly the same DOF."