Hi Heather, let me give your questions a try.
MyHeritage is the parent company for Geni. MyHeritge has a business model that is more similar to Ancestry.com - separate family trees. Every family tree on MH is its own entity with its own managers etc.
Geni's business model is more similar to FamilySearch; a goal of one single shared tree, one profile per person. Geni has volunteer curators to assist in smoothing out technical and genealogical tangles.
Us volunteer curators for Geni have the same relationship with MyHeritage as any other Geni member: none, or if we choose, a data subscription; or if we choose, any of the MyHeritage subscription packages available, of which I have no idea of the current. :)
My Geni tree has been copied to more private MyHeritage trees also (which is fine with me). Therefore I "see" those matches and confirm them back to my Geni tree, which is an exercise in redundancy. :):)
If those cousins choose only to copy over a portion of my Geni tree to their MyHeritage tree, that's their perogative. It's their tree. if I don't want people to use family photos I won't put them on Geni.
It sounds like you inquired of your cousin about her MH tree choices and you got an answer: she has a tree size limit on MH and decided where to "not" include data. For example. If she's used up 225 of her free 250 profiles, perhaps she'd rather save it for a more direct to her line?
In any event, nothing to do with Geni, any more than Ancestry trees or trees on any other site.
Hope that's clearer.