If it were a question of justice or a crime, it might be worth digging up his brother to see if they can get enough DNA for a match. But, depending on how and where his brother was buried, there may not be any DNA to sample. (Sometimes there's literally nothing left but dust or a "shadow" in the ground, particularly if the soil is acidic.)
Since nobody's committed a crime and the existing evidence tallies, it doesn't seem worth disturbing everybody just on the off chance that the newspapers can have a field day over a possible mistaken identity.
I agree. A few days ago I was telling my 10 year old that they were going to do this with Christopher Columbus's grave. He replied, "They shouldn't do that. It's like messing with your leftovers!"