I originally had more nuance in my comment but wanted to keep it simple. In my experience, companies like the ones you describe have a really strong brand (so large volume of branded search) and/or really strong other channels, like SEO. At that point, paid search is a piece of the overall ROI (serving market share or other strategic objectives) and not channel-specific.

Adding even more nuance, that really only describes successful companies. Failing companies _think_ they are profitable, until they quickly aren't. Your experience is very similar to my own. You're 100% right.