What backend do bitcoin sites use?

I'm not talking about payment services like bitpay or coinbase, but the actual technology behind sites like that and even bitcoin currency exchange websites (like btc-e or bitstamp) and faucets.

From what I understand, you have either the option of using the bitcoin daemon (bitcoind) and using the JSON-RPC calls with a language like python, C#, php, etc.

OR

Using the blockchain.info payment system (not completely sure how this works). Does this system use the bitcoin daemon as well in the background?

My question is: are the bitcoind + JSON-RPC calls safe and stable enough to be used by big bitcoin companies such as bitpay or btc-e or something similar, or do companies roll their own custom software (but wouldn't they have to essentially re-develop the bitcoin protocol?)