The under-lever shouldn't open by itself. The lever is mad up of two parts, and in order for the action to open, the two piece which make up the lever must be compressed together to unlatch the action. If the action of your rifle opens without these two pieces of the lever being compressed together, it needs some warranty work. If the lever is working properly though, there is a certain amount of mechanical advantage built into the design so that ejecting fired rounds is not overly difficult. This means that an unfired round would be ejected very easily once the action has unlatched.
What I found upsetting with mine was that after walking with it slung for several hours, I would stop for a break, unsling the rifle only to discover that the safety had moved into the "fire" position. I never had a problem with the action coming open if it was properly closed in the first place. To resolve the safety issue I tried to carry the rifle loaded, but out of battery. It became apparent very quickly that wouldn't work.
When walking through heavy cover, I got in the habit of carrying the rifle in my hands and made sure that my hand was around the trigger guard and lever so that branches or twigs could get inside the trigger guard and inadvertently fire the rifle or unlatch the action.