My experience is that correcting errors on Billiongraves does not push an update on Geni.
Try raising a support ticket: https://help.geni.com/hc/en-us/requests/new
So, you are not talking about a Record Match but are simply talking about the fact that MyHeritage has wrong information -- that is, it is reporting BillionGtaves says something BillionGraves does not say.
This is Geni. MyHeritage errors and shortcomings need to be addressed to MyHeritage.
Nothing Geni can do about MyHeritage Errors.
Tho I suppose it makes sense to warn Geni Users not to trust MyHeritage, or at least do not trust what they report BillionGraves is showing.
About Billion Graves and cemetery names: It is an error/weakness as well in Billion Graves if you start taking photos on a cemetery not yet registered on Billion Graves. When uploaded, the pictures will be attached to the closest cemetery, even if it miles away.
This fixes itself when you register the cemetery itself with area borders on Billion Graves, but if Billion Graves have pushed the registration to third partis like Geni the initial information seem to be stuck.