Legal bods err on the side of caution for no other reason than to get paid more and protect their ass.
The snarkiness of the message does him no favours, and the bigger problem is that designer doesn't necessarily mean host. They might well have contracted him to design a website, put that onto a host (or had it do that by giving him the password) and then he's logged into that to change the document *AFTER* the effect and locked them out of their own website. That *probably* isn't legal.
He doesn't necessarily have a *right* to do that. However, if you do not pay, there are lots of justified means of removal of the service you provided, and ways to recoup your losses beyond just what you were going to charge them. If you take your car into a garage, have work done and then refuse to pay, they can *legally* keep your car until you do - and they can even charge you for storage. My father did it many times as a garage owner, and it's completely legitimate. Similarly, if you don't pay a webhost, they can just take you offline until you do.
A breach of contract, by definition, breaches the contract. Which means there *is* no contract after that point because it wasn't fulfilled (there is an element of reasonableness but that's usually covered by a couple of polite "you haven't paid me"'s). If the company breach the contract and refuse to rectify it, you are no longer bound by the terms of the contract so long as, up until then, you'd fulfilled all your obligations under that contract (with reasonableness built in again). Otherwise, nobody would ever fulfill any contract and you'd STILL have to provide them with free goods / services.
If my bank consistently and wilfully fail to abide by a section of my contract with them, I'm no longer legally obliged to keep paying them. They *can* take me to court, try to start eviction proceedings etc. (so it's an enormous hassle) but they actually can't do much about it in a court of law if they breached the contract. So long as a court sees I was playing fair and not gaming the contract and not being unreasonable, they can't demand I carry on paying (and they end up paying to rectify all the hassle they caused). Of course, I'd be in a ton of hassle and have to change banks / mortgages, etc. and there'd be threats of *EVERYTHING* but it doesn't mean they'd see it through or that you shouldn't tell the debt collectors etc. to bugger off.
What keeps most people from questioning contracts they are in is actually hassle, not legality. Whether it's a mobile phone contract, or an airline demanding you pay hundreds to change their own spelling error, etc. the legality in almost any imaginable reasonable situation is on the side of the consumer. It might not be worth the hassle, but it doesn't mean you're wrong.
I tried to buy a phone from Three. It was a phone + contract that would have saved me money, but it actually never arrived. They wouldn't resend it. They wouldn't refund it. They wouldn't stop taking Direct Debits out of my account. I reported it to the bank as a fraudulent transaction in the end because they did not have my signature (the contract I was supposed to sign was in the box that never arrived!) and, even if they *HAD*, it wasn't signed by me, and even if it *WAS*, they had failed to deliver me a phone and/or service (they admitted themselves that the phone had never been used, and I'd actually phoned up originally to have them block the IMEI as soon as I realised it hadn't arrived so it was unusable in the UK after that). I asked to provide me with a copy of my contract which they insisted I "must have" signed to get that far but they never did so.
Then they started with the crap - they threatened legal action ("PLEASE DO!" was my response, but it never came to anything after months of constant threats), they told me I had to chase it up with the Post Office ('fraid not!), they told me I had to pay for the service even if I didn't have the phone (Nope!), they told me that cancelling the Direct Debit was illegal and a breach of contract (What contract? How so? How is you not getting a phone to arrive in comparison for your obligations of the contract?).
In the end, I refused to speak to them except in writing because they kept threatening legal action - I had to explain that and hang up each time and they'd phone me 5-10 times a day. It took weeks for them to stop calling (with me threatening to report them for harassment, especially after they'd agreed several times to never phone me again and communicate only in writing). Eventually a letter arrived, saying they were going to be so-extra-nice to me that they wouldn't charge me for the "false" Direct Debit cancellation - strange, because my bank were quite happy to take on that challenge for me, and the Direct Debit scheme would have had a whale of a time with that ("We want to take money each month for a service we're not providing and never have provided, please!").
The hassle was *RIDICULOUS*, and for a £10 a month contract. Yep. £10 a month. And the phone was worth about £30. But the point was, my contract obligations were fulfilled (i.e. they took three payments by that time (i.e. £50)), theirs weren't, so I was legally entitled to reclaim my money. Fortunately, the Direct Debit scheme works wonders for that so I just recouped all my money in one ten-minute phone call without their co-operation and then they had to do the running-around to try to get their money back.
Funnily, no court case happened and I never needed a lawyer (my invitation to them to initiate the court case on their behalf didn't go down too well). Strangely, despite their insistence, they had no contract signed by me. Weirdly, even if they DID and could prove it (which would have been a miracle), they breached it first and I was more than reasonable enough to allow them to rectify it (I wanted them to send me another phone, or just refund the £30 and send me a SIM, but they point-blank refused). My reply was along the lines of "Thank you for fulfilling your statutory legal obligations which, up until now, you have been failing to do. Now please stick your company up your ass, T-Mobile gave me a better deal and didn't threaten to sue me for their own mistakes over £10."
It's hassle that an honest lawyer will avoid (i.e. "the case is probably not viable") rather than righteousness. Righteousness doesn't pay off in the real world very often (and is rarely worth the time and hassle). But a breach of contract does just that - breaches the contract and frees you from your contractual obligations.