I don't think it's a stretch to say that the property owner is also responsible for keeping the sidewalk negotiable when somebody illegally dumps a piano on it. From my experience formerly owning property in Philadelphia, it was my impression that keeping the sidewalk clear of anything was my responsibility.
I couldn't find anything about trash on sidewalks in San Diego, but their government page on sidewalks suggest that property owners are partially responsible for maintenance costs of sidewalks:
> Normal sidewalk wear and tear or age damage is the responsibility of the homeowner who can take advantage of the City's 50/50 Cost Sharing Program to help offset the cost of repairs.
https://www.sandiego.gov/street-div/services/roadways/sidewa...
This suggests to me that responsibility for clearing out crap dumped on the sidewalk on your property is probably also the responsibility of the property owner. And if some freak weather caused a blizzard in San Diego, I'd expect property owners would be obligated to clear the snow as well (or pay somebody else to do it.)