Ok so I think I found a conflicting statement in the city ordinance regarding these trees and may leave open the possibility that a homeowner would not necessarily be on the hook to fix the sidewalk...

402.02(A) Says "Sidewalk construction or reconstruction across the frontage (front side, or rear) of a parcel of property shall be paid for by the property owner."

but...

402.02(C) Says "City Tree Roots: Damage to sidewalks solely caused by City tree roots may be repaired and paid for by the City. However, a property owner *may elect** to replace the damaged sidewalk panels at its own expense."*

Note that in 402.02(C) a property owner 'may elect' - but is not required - to pay for damages cause by city trees. However if the tree is a private then the owner must pay for repairs to the sidewalk. So what would stop the property owner from simply refusing to pay to have the sidewalk fixed?