Another poster gave a great answer detailing the common assertions SC/FOTL demand letters earlier in the thread.
I'll address the bolded.
The problem in answering these claims in any official capacity is twofold.
In one sense, answering gives their claims credence. It's hard enough to deal with in an official venue (court, depositions, settlement agreements) where by asserting their claims it essentially stops the proceedings - it's a real issue.
The second problem is that their have been documented cases where written responses denying claims were magically transformed by persons unknown into acknowledgement of a claim or claims.
Like I posted earlier, they're good at turning paper into handcuffs.
To date the best official review of this problem in North America is The Organized Pseudolegal Commercial Argument (OPCA) Litigant Case:
https://ablawg.ca/2012/10/30/the-organized-pseudolegal-commercial-argument-opca-litigant-case/
I highly recommend this as a guide for interested parties.