I would not use deep fakes to refer to counterfeit goods. Deep fakes refers only to artificially generated videos of a real person (usually face, but it could include voice).
Deepfake (a portmanteau of "deep learning" and "fake"[1]) is a technique for human image synthesis based on artificial intelligence. It is used to combine and superimpose existing images and videos onto source images or videos using a machine learning technique known as generative adversarial network.[2] The phrase "deepfake" was coined in 2017.
Because of these capabilities, deepfakes have been used to create fake celebrity pornographic videos or revenge porn.[3] Deepfakes can also be used to create fake news and malicious hoaxes.[4][5]
I didn't read the parent post as using it that way - I believe they're saying that any claim that "supply chain security" (of videos) will combat deep fakes* isn't necessarily a credible model of security considering that the "real" supply chain (of physical goods) isn't apparently particularly secure.
I don't think I actually agree, however. Things like hashing and cryptography make me inclined to believe a digital 'chain of custody' is easier to prove and validate than a physical one.
( *I'd never heard this before, but it's an interesting claim )