My Dad says he vaguely remembers what he thinks is a Columbo episode. It involves identical twins, that people are getting confused between, and he thinks has something to do with an inheritance. It is NOT 'Double Shock' as we watched that last night. He says that he can remember it fairly well, but can't remember anything to do with the detective, so he has to assume that that it is a Columbo.
While I suspect you are correct that Luke's dad is thinking of another detective show, I believe the blind man and his brother in "A Deadly State of Mind" were twins.
I dont't think so: they are brothers, but not identical. In fact, the characters are just brothers, not the actors, without any kind of real relationship.