I'm conflicted.. I, personally, would hire the well-rounded "generalist" individual every time. Yet, I know that as a job applicant, most hiring managers don't have much vision when it comes to developing a well-rounded team.
The rest of interviewing should be done by actual engineers, peers and colleagues of a prospect employee.
The best engineering teams I've encountered are ones that have an Engineering Manager. The hierarchy is Project/Program Manager -> Engineering Manager -> Engineers. The engineering manager (of technical background) cultivates the engineering team, instills best practices and makes final decisions, without having to sit in endless meetings with the business side (the program manager's job). The engineering manager is usually the hiring manager for more engineers.
It's not a sexy, flat organization, but day-to-day operations are less like herding cats and more about promoting technical excellence.