Both sides acted childish, but I can't see why a negative outcome would come as a shock to anyone.
Let's say I flip out in my local bank branch. They're perfectly justified in calling the police, because it is a bad idea to yell at people at the bank - but they would not be justified in closing my account and keeping the money to "teach me a lesson", and that is essentially what happened here.
I find it a shocking lapse of professionalism to do anything like this, and I find it incomprehensible that an adult could think it was justified. Seriously. You just don't act like this in the real world and hope to stay in business - sooner or later this attitude will kill you. Customers do flip out and tell you to fuck off, they just do. You either learn to act like an adult about it - maybe step away from Twitter for a while - or you quit, and get a job that doesn't involve interaction with customers. Or co-workers. Or anybody else that might harsh your fragile calm.
"Fuck you" then sounds like the equivalent of "kindly delete all my data", no?
Personally getting pissed off for someone for being a dick? That's fine. Using the business to basically get revenge on them for being a dick? Not fine. You're not there to punish customers for being pissed off.
Guys aren't gonna get very far if they have a paddy with every irate customer that comes along. And everyone who's been in a customer-facing job knows they far outnumber the pleasant folk.
And you know what? I bet the dispute wouldn't even have occurred if the CS rep just said something like 'sorry, we cannot discuss the details of other clients' accounts'.
