I cycle about 2,000 miles a year on the streets. The only collision I've ever had was when I was hit by a car while riding on the sidewalk. Old lady in a sports car not paying attention. There's just too many people pulling out of parking lots that become a hazard. Too many blind spots for those drivers. Too many obstacles like crowded bus stops, electrical boxes, poles, abandoned shopping carts, etc. In the scenario where I got hit in the sidewalk, there was a bike lane I should have used instead.
There are a couple scenario's where i'll go on the sidewalk:
1) It's late at night, and the sidewalk has very few pedestrians, and cars passing through it. Late at night, there's more chance of DUI drivers, or cars full of teenagers that like to mess with cyclists. I've been hit with eggs, bottles of beer, and have been threatened, just while minding my own business, all these incidents happened at night. After dark I like to distance myself from cars as much as possible. 4 cyclists have been killed in my city this year, two days ago it was a DUI driver on the same block I ride in.
2) If I'm on a street that has very heavy traffic, and the street has no bike lane, no shoulder, and the car lane is less than 8' wide. I would rather go on the sidewalk than overtake a lane. In the area where I live, drivers almost never see cyclists take lanes, and the few times I have done that, they became confused and enraged and blared their horn at me even though they had another open lane to use. They simply don't understand the concept of taking a lane, or the reason why it's done. It's not worth it if there's a sidewalk I can use.
I don't agree than using a sidewalk is always the less safe option 100% of the time. I think you have to judge the situation for yourself after considering the factors.
Things like how wide the sidewalk is, and how much car and foot traffic are along those sidewalks are things that need to be taken into consideration.