You could make a more than coherent case. I probably wouldn't, because we don't know exactly how good some of his opponents were, owing to the paucity of records from the era. They guy was lineal in three of the original weight classes, and great in all of them.
Who can definitively say, all i know is is he was the best boxer to have been born in Cornwall, and he did mightily fine on the world stage at all that fisticuff malarkey. Now if he had stayed in Cornwall and trained on a diet of Cornish Pasty's, he would have matched Jefferies for size at the scales.
Maybe as good a canditate as anyone for p4p between the decline of George Dixon and the rise of Joe Gans. If there had been a LtHvy title throughout Bob's career he might have been a champ for a dozen years. Let me put it this way: Bob Fitzsimmons should be in the discussion for any thorough consideration of a p4p short-list for gloved boxings' history.
I have seen it argued by historian Tracy G. Callis that Fitzsimmons was the greatest ever. I can see the logic behind it, even if I don't buy it wholesale. Imagine if Roy Jones Jr., the closest modern equivalent to "Ruby", won the genuine middleweight and heavyweight crowns and then it took the greatest heavyweight of his generation to put an end to his reign at 36 years of age. Then Jones improves on his performance three years later in a rematch but still loses and then captures the Light Heavyweight Championship at 40. I understand the eras between Fitzsimmons and Jones make for different contexts and things don't translate neatly because of it, but it does give you a sense of how special Fitzsimmons was. I remember reading Joe Gans' biography and him citing Fitzsimmons as being influential in developing his own style after attending a number of his exhibitions.