> This is quite novel idea, indeed. Can you, please, cite respactable source which says that you must "force users to pay" to qualify for "open core" label?
GP is right, 'open core' is a term used to describe a particular business model. As a business model, it speaks about how to make money.
Of course, you can use the two words 'open' and 'core' together and mean something else. It's confusing though, to people that are familiar with the term as it's currently used.
If you want some verification for the proper use of 'open core', just google it. The first result I got there is good enough: