Is it really safer to ride in the road than on the sidewalk?
In most scenarios, it is not safer for you to ride on the sidewalk. This has been demonstrated numerous times in numerous studies. I won't attempt to site individual studies here, but I will sum up the reasons. 

One is that you create more potential points of impact. When you exit the sidewalk to go through an intersection, driveway, or parking lot entrance/exit you are in danger from the cross traffic as well as parallel traffic making turns. The latter danger is greatly reduced if you ride in the street simply because you are in the same lane as those drivers.

Furthermore, drivers simply aren't watching for cyclists on the sidewalk. Cyclists typically move much more quickly than pedestrians and drivers aren't prepared for that. Cyclists seem to "come out of nowhere" as compared to slow moving pedestrians. Pedestrians are also able to stop much more quickly if a driver doesn't see them.

All that said, there are some situations where cycling on the sidewalk is safer. Personally, if the speed limit is under 40 mph, I typically ride in the street. If it's over 50 mph, I typically ride on the sidewalk. If it's between 40 and 50 mph, I judge the road based on how many entrances and exits there are, how wide the shoulder is, how much traffic there is, etc.

Mike Baranczak said it beautifully in his comment, "Riding on the sidewalk is always a bad idea. But sometimes riding on the road is a worse idea. You have to decide based on individual circumstances."