I think it's like 'needs work' in a pull request. What one person sees as just honest feedback another sees as starting a fight that didn't need to be one. And a lot of tech people have learned to hit back when they think they're being bullied. Because bullies don't stop until they're bleeding in front of witnesses. Let's get this over now instead of dragging it out.
You've escalated where threat of escalation should have sufficed. Hey we need you to change your site to make it obvious this is a fan site and not ours. Otherwise we'll have to send a properly lawyery letter in a few weeks if we don't hear back from you about a plan.
One of these throws a person's life into utter chaos. The other gives them time to be a grownup about it.
From a lawyer perspective though, a cease & desist is a threat of escalation.
A lawsuit is the escalation. A cease and desist is a strongly worded letter that isn't really legally binding or anything.
The issue here is just impedance mismatch on the language. The legal department is used to doing things in legal terms, and probably sends out like a lot of cease and desists. And most of the targets of those also have lawyers who are speaking the same language, so it works. Just when it's a random individual getting the letter, there's a lot more confusion.