I just read a report on a sample analysis (355 cases); over 99% of those who died in Italy suffered from other illnesses. Here are the exact numbers:
Ischemic heart disease: 33.0%, Atrial fibrosis: 24.5%, Stroke: 9.6%, Hypertension: 76.1%, Diabetes: 35.5%, Dementia: 6.8%, COPD: 13.2%, Active Cancer in the Past 5 Years: 20.3%, Chronic Liver Disease: 3.1%, Chronic renal disease: 18.0%
Percentage of those who died with 0 other diseases: 0.8%, With 1 other disease: 25.1%, with 2 other diseases: 25.6%, with 3 or more other diseases: 48.5%
Link to the official report: https://www.epicentro.iss.it/coronavirus/bollettino/Report-COVID-2019_17_marzo-v2.pdf
Doesn't make it less terrifying though.