Yes, pretty much, and for the reasons you gave. Some undergrad programs by design are exploratory, where you can go, try out different things, then decide on your major. And it might be any of a long list of diverse things the college offers.
Others are more designed for people who already know what they want to do in at least a narrower range, and from the start the experience is really organized around that.
One of the confusing things, though, is one institution can have different undergrad subdivisions that function in different ways. So, it might have some specialty schools and then something like an Arts & Sciences subdivision. And then sometimes there isn’t much barrier to moving between schools, but sometimes there is, and sometimes it depends which school you are talking about.
And conversely, I agree even if you want an exploratory model, it needs to have anything you might want to explore. So, in your D’s case it makes perfect sense to eliminate exploratory colleges without engineering (although I would note Mudd is not the only LAC with engineering).
Of course as usual, this is pointing to all generic rankings not really making sense. There is just far too much variety in focus, curriculum structure, internal transfer policies, and so on. So you need to figure out which colleges would work for you, and then you can compare among them. And in many cases, there will be no published list that looks like that, and that’s fine.