It seemed that the databases should only be used locally. No other computers should be allowed to connect to the local databases.
I changed this file in this way:
# TYPE DATABASE USER ADDRESS METHOD
# "local" is for Unix domain socket connections only
local all postgres trust
# IPv4 local connections:
#host all all 127.0.0.1/32 trust
# IPv6 local connections:
#host all all ::1/128 trust
# Allow replication connections from localhost, by a user with the
# replication privilege.
#local replication postgres trust
#host replication postgres 127.0.0.1/32 trust
#host replication postgres ::1/128 trust
According to this page,
"HBA stands for host-based authentication."
local is a record which "matches connection attempts using Unix-domain sockets." In addition, "without a record of this type, Unix-domain socket connections are disallowed."