Serena’s family made the remarks during a visit by the news network’s Beirut Bureau team in Lebanon.
The family members refused to appear on camera but said they suspected the Turkish authorities were somehow responsible for her death.
Her parents said they would pursue the matter legally.
On Friday, Shim, an American citizen of Lebanese origin, told Press TV that the Turkish intelligence agency had accused her of spying probably due to some of the stories she had covered about Turkey’s stance on the ISIL terrorists in Kobani and its surroundings, adding that she feared being arrested.
Earlier, Press TV news director Hamid Reza Emadi called on the Turkish government “to find out exactly what happened” to Serena.
Shim, a mother of two, covered reports for Press TV in Lebanon, Iraq, and Ukraine.
She was on a mission on the Turkish side of the border across Syria’s strategic town of Kobani to cover the ongoing war there between the ISIL terrorists and Kurdish fighters.
Her car collided with a heavy vehicle upon return from a report scene in Suruç, a rural district of Şanlıurfa province of Turkey.
The identity and the whereabouts of the truck driver remain unknown.
Shim said she was among the few journalists who had obtained stories about Takfiri militants’ infiltration into Syria through the Turkish border, adding she had gained access to images showing militants crossing the border in trucks belonging to the World Food Organization and other NGOs.