Am Arduino is not a production solution. It's great for prototyping, but to expensive for mass production. You go with something as small and cheap as possible.
I think the parent was talking about Arduino as a software platform, instead of the Arduino hardware. The software itself will run on pretty much any of the 8 bit avrs, even things like the ATTiny45.
You can totally use the Arduino in production, and it's happened quite often. The core of the Arduino is just the ATMega8 micro, which is only a few dollars - Arduino is just a nice programming environment and set of libraries for it.
Can you? Sure.
Should you? Oh, sure, if you want a very expensive piece of hardware in your product.