How do you accept bitcoin? Please enlighten us.
I didn't say you shouldn't use wallets, just don't use the naive approach of having a plain wallet in a computer that's exposed via bitcoind. That's asking for it.
Cryptography is hard, but you can use this for instance:
http://bitcoinarmory.com/using-offline-wallets-in-armory/
It's already prepackaged for you. Give it a good read if you don't know it. Free, Open Source, etc. And the author is a nice chap.
It's not the only way. But whatever you do, just don't keep a massive hot wallet in a server that's online. They will find it and if you move enough money they will put massive amounts of effort into hacking it.
EDIT: BTW, you do realize that Armory is a front-end to bitcoind, right? You still have to run bitcoind for Armory to work.
From their Github page:
"Armory has no independent networking components built in. Instead, it relies on on the Satoshi client to securely connect * to peers, validate blockchain data, and broadcast transactions * for us. Although it was initially planned to cut the umbilical * cord to the Satoshi client and implement independent networking, * it has turned out to be an inconvenience worth having. * Reimplementing all the networking code would be fraught with bugs, * security holes, and possible blockchain forking. The reliance * on Bitcoin-Qt right now is actually making Armory more secure!"
You can have a computer with a firewall and a custom protocol connected to another system, and still get hacked, if you don't put in place the sort of measures Armory uses.
Read carefully what you quoted: "it relies on on the Satoshi client to securely connect * to peers, validate blockchain data, and broadcast transactions * for us" - that is not the actual problem when you have your server rooted. The problem is KEYS. Key generation, and key storage/management. Which no other common solutions that I know do in a way that won't get your arse robbed if the computer storing the wallet is compromised. Which I think is a big deal.