From the BBc website it seems that it is her aunt and grandparents that have been debnied visas. Website goes on to say:
"Explaining its decision to the three family members, the Home Office said it was "not satisfied that you have demonstrated that this will be a simple visit of three months or that your intentions are genuine in wishing to travel to the United Kingdom".
The decision papers said all three had been refused entry clearance in October 2013 "partly due to economic ties to Zimbabwe", which had not been addressed in the more recent application. "
So basically they are worried that this little girl's family are using of her death as a pretext to settle here

Signed.