No-one should be accepting parts based solely on the presence of a C of C - from an independent or even an authorized distributor. You should have a QC plan in place that includes comprehensive visual inspection, microscope, x-ray, XRF, decapsulation, solderability, etc.
Some standards to follow in regards to inspection techniques: IDEA 1010B (ICE-3000 certification) AS9120 CCAP101
I'm sure there are many I am not mentioning, but these should be applied at the very least.
With the recent SASC uproar over counterfeit parts being found in US Government equipment, it is extremely important for any and all companies involved in this industry to verify the authenticity of any and all devices that come through their door.
In my opinion as an experienced inspector, if you're not inspecting you shouldn't be in the business. Gone are the days of bringing in devices and sending them to your customer without a glance. Due dilligence is required by both the distributor and the customer.