If this was memorialized in a Court order, then it probably is a public record. Depending on the state, you might be surprised at what you can find in Court records, many of which are available to the public. As for the "random busybodies," if I were in the position of this elderly woman or her siblings, I'd be very grateful that there still are such "busybodies" in the world to look out for another person who needs help.
This was reported to be a "settlement", which is not usually used to describe a court order. Family and probate court matters generally do not become part of the public record, unless certain criteria are met. And when they do, it is in a VERY formal way -- i.e. people can get a copy of the official documents -- not some judge as libbing to some total stranger who calls him up.
Note that most of the probate court level Terri Schiavo records were sealed. What was public was the appellate records, which contained only a handful of personal facts, and were primarily about the courts' interpretation of legal procedures. Other information about Terri got into the public domain by members of her family sharing it.