However, they have told me what I interpreted to mean that if someone improves it but uses it then they need to license the underlying patent. That just makes sense, it's required in order to implement their concept.

And in reverse the original company can keep doing whatever they want as long as it isn't covered by the referencing patent. Makes sense to me there too, if they come up with some other clever way to make it good enough more power to them. There's no reason for them to pay some other people who patented something they don't use.