Pretty much every job offer I've gotten has involved walking into a manager or interviewer's office and pointing out things he can do better with his business. It's often not core stuff, but I'll frequently point out UI improvements they could make, or new technologies they may want to take a look at, or new algorithms & data structures that can solve their interview questions. And on the flip side, I enjoy learning about new businesses and new techniques they're using to the greatest extent that they'll share them with me.
A-players are not threatened by this. B-players are. I've found that it is generally good for your career to try to work with A-players whenever possible and avoid B/C/D/F-players.
I've had a similar experience. I've found out, though, it isn't really what you say, it is how you say it. Be assertive without sounding arrogant and pushy. If you go in to an interview and pretend you are a consultant selling your services, and not someone who is desperate for a job, then chances are better you will get an offer. Now part of this is reading body language, to see if what you are saying is triggering a happy emotion in the person interviewing you. For example, in my current position, it was apparent that things were in chaos. I started mentioning some automation tricks, and that lead into a strong emphasis on repeatable processes. Turns out, that was the key phrase that got me hired -- I found a dozen ways of giving the same message of automation, repeatability, and trackability. In a previous position, I had sold the hiring manager on a design for a web based user account automation system (kind of accidentally). Turns out that was their biggest pain point at the moment, handling a huge stack of account request forms. So either I was very insightful during the interview process, or extremely lucky. Or, I happened to take my vitamins that morning.
A-players are not threatened by this. B-players are. I've found that it is generally good for your career to try to work with A-players whenever possible and avoid B/C/D/F-players.