I'm not the OP, just someone giving my advice.
I'm sorry, but I agree it's poor advice.
The TOC has nowhere near enough evidence to take this to court. Saying anything just increases their evidence. Responding actually acknowledging that the Railcard was misused provides perfect evidence to start looking at a prosecution, not to mention plenty if they instead try a civil claim (which holds a much lower standard of proof).
Based on the sample size we've seen here, they will have sent out hundreds if not thousands of these emails. I expect that it's an automated system that's sending out the escalation emails and only responses are reviewed by a human. I would expect a majority of emails they send will remain unread or with no response.
What will happen is that they will send a few more threatening emails, probably say they'll pass the case over to BTP and that will be it. BTP do not have the resources to investigate hundreds of cases with no evidence.
The TOC may try a civil claim (which they are allegedly starting to do, not that we've seen much evidence of that here) but in comparison to a criminal case this is relatively low stakes and can be dealt with in the unlikely event it comes up.
In most of these we've seen, the TOC clearly doesn't even know the full name of the purchaser - let alone their address.
It is not in the OPs interest to reply to the emails in any form.
