The sheriff’s deputy who shot and killed Sonya Massey claims he feared she was going to throw a pot of boiling water on him, but based on the horrifying police body cam … her family and their attorney aren’t buying it.

Ben Crump is representing Sonya’s family, and joined us on “TMZ Live” Tuesday alongside her father, James Wilburn, and we asked about their takeaway from the body camera footage showing her fatal interaction with law enforcement.

Ben says Sean Grayson — the Sangamon County Sheriff’s deputy charged with first-degree murder — doesn’t look like he’s fearing for his safety in the footage, because instead of moving away from Sonya as she handles a pot of boiling water, he moves toward her.

Crump thinks Grayson was moving closer to Sonya, so he could get a better shot.

Remember, Grayson fired 3 shots, one of which hit unarmed Sonya in her head, and then told his partner not to bother with rendering her medical aid as she bled out on her kitchen floor.

Grayson said he feared for his safety, but the Illinois State Police say their review found his use of force was NOT justified.

Crump’s taking it one step further … and thinks if Grayson was really afraid, he would’ve moved away from Sonya and not toward her.

Sonya’s father says he was, at first, misled about this being an officer-involved shooting — and tells us he never thought his daughter would join the likes of George Floyd, Breonna Taylor and other Black people killed by police.

James says his daughter’s death has been especially hard on him … and he’s certain it would have caused his heart to fail, if not for a recent bypass surgery.