I got that information from someone who waned to take their California cdl test in an m925a1 and was told they couldn't, that it didn't have the required equipment for the pre-trip checks test out.
fortunately I have no first hand experience with California's CDL. Artisan does, ask him. Quickfarms is highly knowledgeable on the topic as well.
I looked into this several years ago when I needed to get a new CDL.
CA does not require the DMV examiners, or CHP commercial officers to have a CDL. Competency varies widely between personnel.
When taking the test it is recommended that you use a truck they are used to seeing, hence a CDL school truck. If you bring a truck they are not used to seeing they could perform a full DOT inspection or fail it for some simple item. This could lead to a red tag and tow. They could simply refuse to let you use the truck for the test because it does not have CA or USDOT numbers, current weight sticker, does not have a current CVSA sticker or has historic plates.
One big issue these truck have is the wedge brakes. How do you inspect the slack adjusters? You can't because wedge brakes do not use slack adjusters. So you will loose points on the pretrip for this and the whole issue could confuse and distract the examiner and get them in a bad mood.
The other advantage of using a civilian truck is comfort. This includes the seat, heat and air conditioning and background noise. You need to be able to hear and follow the examiners instructions, failure to do so will cost you points or could lead to an immediate fail. A comfortable DMV examiner is better for the testee.
The next issue is either series of military 5 ton will lead to a restriction on your license. You could have to redo the entire process to remove the exception.
Your results may vary by DMV office.