brain stem hemmorrhage

3 weeks ago my co-worker who did not have any symptons  other than being treated for having a bad cold and sinus infection died.  She had a terribe coughing spell at work and said she had a pain in the back of her head low neck area.  Moments later she was vomitting and un-responsive.  After calling 911 she was taken to the hospital where a cat scan was done.  They said she had a hemorrhage to the brain stem and her brain was full of blood.  There was no brain activity.
Her family after a few days decided to remove the life support.  She died a few hours later. No autopsy was done because of her religion.  She was 48 years old.   My question is could a severe coughing spell cause such a thing?  My co-workers and I are are left stunned and looking for some answers.  Any light that you could shed on this would be greatly appreciated.  Thank you.