An EEG is NOT an accurate tool, by any means, to make this kind of determination. Not even close.
ct scans are by convention read looking from at the bottom(feet) up, so what is on the viewer's left is on the patient's right. neuroscientists don't like this convention, preferring a top-down view, but it was made when radiologists ran the imaging machines and we're stuck with it. generally a board-certified neuroradiologist, neurologist, or neurosurgeon should be reading head ct scans; if it is not interpreted by one of these, i am generally suspect of the results.
if the EEG is ECS (electrocerebral silence), then she is by definiton brain dead. however, since by video she doesn't even come close to meeting brain death criteria, and activity such as she exhibits even if "reflex" should show up on EEG, i suspect an amateur interprectation of the true results. Terms such as "flatline" are not used by knowledgeble eeg interpreters.
do you have a link to the ct images?? the tube may be a shunt or (unlikely)may be part of the "brain stimulator" she had implanted (would need the op notes to see what type and where it was inserted). occasionally as a last ditch effort, even if the ventricles are large by what is suspected to be ex vacuo from atrophy, a trial of decreasing ventricular pressure may be tried, based on some questionable french literature with hydrocephalus....
btw, thanks for bringing up this aspect of her diagnosis; evidence supporting the depth of her dysfunction looks pretty shoddy.