Ask HN: should we be publishing screenshots?

Our company has a personal health records platform that we are proud of because it is user friendly and powerful. It is built on top of open source software and the company that created that software wanted to feature us as one of their partners. I am pleased by this vote of confidence and was trying to decide what screenshots to share with them.

However, in the last week, two CEOs of different start-ups that I was interviewing for a book I am writing refused to provide me with screenshots of their products to publish in the book. Both said their user interface is a trade secret that they did not want to share.

I cannot figure out if they are being naive (for missing out on an advertising opportunity) or I am being naive (for being ready to give away my own company's "trade secrets").

Any advice on what I should do?