Can sewage smell penetrate indoors because of inadequate venting?
I would say NO, the vent is not the problem. A more likely culprit is a bad wax seal. I have found toilets with no water leakage and big gaps in the seal were someone tried to use silicone to seal the flange. No leakage and constant sewer smell. I pulled the toilet and was amazed. Cleaned probably a full tube of calking (calking gun size) out installed a .99$ was ring and the smell was gone. 

Any residual smell may be from urine in the flooring and there are chemical treatments that can fix this. 

Last if there is a floor drain it may be the cause of the smell, pour some water in the floor drain then add a cup of cooking oil this will keep the water in the trap from evaporating.
A clear vent even in a 3 story would not cause the smell you describe.