This would be a big red flag to me if it applied in the general sense at a company. Stuff that's open-sourceable is generic enough to not contain trade secrets, so what is there to hide? Though if it's a question of maintaining the project, I can understand a company deciding not to invest in maintaining the project (though I still think it's good when they do).
In my own experience, my employer does not prioritize open sourcing internal projects, but at least every time I've asked if I could open source something, it's been all thumbs up as long as it doesn't get in the way of normal business priorities. It's just a question of whether I feel it's worth it to me personally to become an open source maintainer.
Aside from that, I've contributed back to open source projects we use at work because there were some issues we found in the process of doing the work and that's resulted in improvements to those projects and a nice little side note on my CV. Even in a super draconian environment, given enough time spent working with open source dependencies, opportunities like this are likely to come up.