Solution
The automated Calibration Executive procedure for each device is only tested by NI for use with the specific recommended standards equipment listed in the procedures. NI does not guarantee automated procedure compatibility when using standards equipment of a different model than recommended in the procedure.
Calibration Executive does allow unsupported standards equipment for any device procedure that lists support for manual mode. In manual mode, Calibration Executive prompts the user to make manual measurements and input results for any steps which use the unsupported instrument. When using an unsupported standard, it is crucially important to ensure that it meets the requirements listed in the device calibration procedure. Example for the PXIe-4041 device calibration procedure:

Since this procedure supports manual mode, you can use an unsupported DMM to calibrate the device if it meets the highlighted accuracy/resolution requirements.
If Calibration Executive has a driver installed for a standard other than what the procedure recommends, it will still allow you to choose to use the non-recommended standard during standards selection for the automated procedure. If the equipment meets the requirements, the procedure may still execute in automated mode successfully, but operating Calibration Executive in this way is not supported and could result in procedure errors or failed calibrations.