Thanks, Mike, for bringing this forward and your other comments.
Regarding the references to steam and fire, they are saying, we don't use a column still (Coffey or patent still) to rectify. Such a still uses steam to separate alcohol from water. The steam pours in from the bottom through perforated plates and meets the falling wash, separating alcohol very efficiently from the water in the wash. Rather (they are saying) we use a copper still heated by a (real) fire burning underneath it. And we rectify, too, that way. In other words, they double distill in traditional pot stills (the way Scotland still does for malt whisky). This ad was an assurance to readers that the whiskey of this house would still taste like whiskey because some of the flavourous fusel oils and other congeners would have gone over with the water through the coils and condensed in to the final spirit. The efficient column still would leave all those behind in the spent wash.
Double-distillation is still used for bourbon, but from the column still (which may contain some copper) to the thumper or other secondary distillation method. Columns can be operated today in a way to reduce their efficiency and thus act much as a first pot distillation would do.
The term OFC (Old Fire Copper) can be seen on old bourbon and rye labels and was a sign of quality. To this day in Canada, Barton's makes in Quebec Schenley OFC. I once read OFC means in that regard, "Old Fine Canadian" but I think that may have been a later embellishment, and the name denoted originally the process proudly claimed in this 1858 advertisement.