I would say yes. I have graveyards for each of my sub-hoods, and one for my main hood. If they died in Downtown, they get 'buried' there!
I don't know what you could do to fix it-I would suggest having Natasha go and put the grave in her inventory and 'bury' her in the main Pleasantview, but don't know if that would cause any more problems, such as duplicate character files for Coral.
You don't need anything fancy unless you want a fancy community burial lot. My Uni burial ground is just an empty community lot