I suspect that the ABPI is possibly the genesis of this, but it's hard to say. It is a relatively common "ambulance-ism" that patients with an aneurysm somewhere in the thorax will present with unequal blood pressures. The degree of difference required to be significant is seldom quantified, nor does there seem to be much grasp on the pathology that would be required to give rise to a difference as I usually hear it with reference to abdominal aneurysm.
I never heard of "difference in pressure in the arms" prior to this. But in a quick analysis of how it would work and if anyone should care, this is what I think.
The most common locations for aneurysms are the abdomen and the circle of willis. If this helps look for a thoracic aneurysm, it may not meet the time/benefit test.
In a pseudoaneurysm, the most common location is the acending aorta. It is possible that the infiltration of the media could block the brachiocephalic or subclavian. But that is not reliable as arteriosclerotic occlusion could do the same. (which is more likely in the limb artery than in the aorta anyway.) It doesn't account for anatomical variances or coarction of limb vasculature either.
All in all it sounds nonsensitive and nonspecific. Waste of time.