Coffee contains thousands of chemical compounds, which are mostly trapped by a paper filter. Metal AeroPress filters and even cloth types will allow more oils and other compounds to flow into your cup.
The oils locked inside coffee actually provide additional flavor to your final brew and are safe in moderate amounts for most people.
However, some studies have suggested that oils found in coffee can cause a moderate increase in cholesterol. But, there have been no links that suggest that coffee consumption increases the risk of heart disease.