While the pocket dimensions have a reasonable tolerance range, the specs tend to add to the confusion when the range on the primer height shows values that can exceed the pocket depth.
What the SAAMI spec is missing, is an explanation that the overall height of different primers vary due to the design of the cups and anvils. Primers are designed with differences that all assume some amount of compression in the height upon installation.
Some models are designed such that the initial anvil height sits high in the cup, and others can start partially telescoped into the cup. What isn't always visible, is how the cup and anvil will sit in relation to each other when the primer is installed such that the cup is at least 0.003" below flush in the pocket.
While the SAAMI note mentions a minimum installation of "flush" to 0.008" below, I would always recommend a minimum of 0.003" below flush as a nominal goal to have the allowance for variations that might mean a sample may result in less due to dispersion from friction, defects, or dimensions.
I'm getting more variation in primer seating depth (using Accuracy 1st tool) than the numbers above would indicate. Either there's more variation in the primer heights than my ad-hoc sample showed, or the rim thickness is throwing a wrench in the works.
I'm not sure how much variation you are finding in the assembled dimensions, but there are always some small variations in the rim thickness. However, the rim thickness variations should be less than 0.002" and are often way less than that, which should prevent most "fixed" primer seat tooling from creating a variation of more than 0.001".
Sometimes, folks seat by feel and sometimes their tools are set to a "fixed" dimension. If you are finding large variations in the seating depth with a fixed tool, check the rims for damage. Often a semi-auto can be hard on brass to the point of bending rims. If you are seating by feel and seeing large variations, best to inspect with a tool like the Accuracy and determine if your "feel" is "calibrated" and that the primer pocket depths are uniform.