"My take:
I don't see how Dad can be responsible since he's doing everything in
line with the law. Once it gets to the street is up to the local
'whatever' to dispose of that water safely. Right? If they were
allowed to hook into the storm sewer - OK. Case closed. "

The first obvious question is whether discharging a sump pump into the
street is allowed in your particular town. If it is, then he's
certainly on safer ground. However, if a particular home pumped water
out in a fashion that caused a hazard which resulted in an accident,
it's anyone's guess as to whether the homeowner could be held
responsible. You'd need a good legal opinion and even that might not
be sufficient. If someone sues, it could be up to the courts to
decide.

If pumping water into the street is creating a potential hazhard, I
would look hard into other options, rather than worry about possible
legal problems.