Gotta tell you, that "giving a shit" scale isn't true in my case. I work for an agency and we give much more of a shit about our client than the client's internal devs do... about the code, about the business, you name it...
That said, using an agency to build your startup probably isn't the best idea for so many reasons.
Also it's a big variance of caring, some big agencies do care a lot but they're rare and hard to find. Some staff turn up late and are hungover every other morning. It's a wide range but I was trying to average it out!