FAR 91.171 allows a pilot to use independent VORs to do the VOR check as opposed to using a testing facility. The reg says as long as they are within 4 degrees of each other the pilot is good to go. But why do they allow this? What if they were both within 4 degrees of each other but both were also off about 45 degrees when actually tuning to a VOR. It seems like using the dual VOR check tests the precision relative to another unit but not the actual accuracy of the system.
You're correct that a dual check does not directly assess the accuracy of either of the individual systems to the true radial the aircraft is located on.
However, the probability that your example of both of them being in error by 45 degrees and also within 4 degrees of each other at the same time is improbable. It is likely that the FAA has examined the risk associated with the different methods of verifying the VOR's accuracy and determined that this is an acceptable risk due to the low chance of such a scenario coming to fruition.
It's important to remember that each VOR is a separate system, and they do not share common receivers.