Agreed with Ryan M. on this. In my experience in the nut industry, (and it is probably different for each industry) some of our customers required COA's but didn't even know what they wanted/needed. We received COA's for all raw inbound nuts. That seems pretty standard and I never had an issue getting them. However, most of the time I didn't know much of the published data on them. I would compare COA's from different loads from time to time and notice the numbers never changed or they put the wrong lot number on the form (most likely a copy and paste job) so who's to say they are correct unless we did our own testing. Which we didn't but looking back now we probably should have at least spot checked some loads.
Bringing this back full circle, I think each situation is different. Figure out what you need and what your program requirements are. Determine what you are comfortable with getting from your supplier whether it's just a CoC, roaster validations, COA's, etc. It probably wouldn't hurt doing some of your own testing every so often as well.