pitot failure is known to have occurred but this has no effect on the vsi , the pitot has two sources impact which can get blocked and static the vsi uses the static side
However this could all have been avoided had the crew a handheld gps to crossreference with as this wouild have given them an accurate speed readout as well as height. I have always carried one when i fly along with a handheld icom radio, as long as i have them I will never use them but you can guarantee the day I leave them at home something will go west. However it doesnt get away from the fact that the crew were not up to the job sadly