You have to wonder if this part was approved by a qualified lawyer at all. A trade secret would describe proprietary knowledge of how to implement the technology, but would have no protection under patent law.
They also repeatedly claimed "DisplayLink is not a member of OIN" when it actually is, and later when they acquiesced to the cease and desist, one of the actual engineers from the company tried to review the PR to ask for changes. It's not clear anyone there has any clue what's going on!
I suspect they know that, but it reads as if they were just lazily tacking that claim on for effect. This isn't a petition to a court, this is just a demand letter. Listing out a bunch of scary damages is how demand letters often work. They don't have to go into details as to the basis of their legal claims.
Yes, but this claim is not that... It sounds like they're making an argument about trade secrets, without explicitly detailing the legal justification for it.
You definitely don't need to cite the legal justification for every demand you make in a demand letter.
You don't even need to have a valid justification to make a demand in a demand letter... it is common and normal to make arbitrary demands... they are negotiations.
Trade secrets aren't protected by law. That's why they aren't disclosed. If someone lawfully reverse engineers your trade secret, its secrecy disappears without legal recourse. Decompiling a binary for RE interop purposes is legal in the US.