I guess the answer turns on what is happening at the point of exposure, Professor. For if bacteria is altered by exposure to mutagens, I don't think it's fair to simply assume that the alteration is a purely "random" event. Rather, the alteration may well proceed according to "rules" -- information. The transformation of the bacteria in adaptation to new conditions can be seen as an instance of self-(re)organization in response to changing conditions, a/k/a ("rule-based") emergent behavior. Function may likely be altered commensurately. It is conceivably this new, "novel function" that is the key to understanding changes in the bacteria's resistance to the antibiotic.
I'm not clear on why you make the distinction "new" antibiotics. The above statements refer to bacteria that were not resistant to a given antibiotic prior to exposure to the mutagen, and then were found to be resistant to the same antibiotic afterwards. At the level of the bacterium, there is new function, but not future function -- from the standpoint of the bacterium, the altered function is the "new now." The subsequent finding that the altered bacterium was resistant is the future event that "discovers" the change in function. This is not a "future function," strictly speaking, but a recognition that an existing function has been modified, at some time after the alteration occurred.
In other words, the antibiotic was "looking for" the preexisting function, but did not find it, and so could not do its expected "work." A new antibiotic would have to be found to address the altered functional picture.
Just a speculation...in the manner of an IDer, I suppose.
The investigators took a monoclonal culture of a bacterium which was penicillin resistant, thanks to the enzyme penicillinase. They exposed the culture to a mutagen and to another antibiotic, I think erythromycin, to which the bacterium was originally not resistant. Most of the bacteria died off, but the remaining living and multiplying bacteria were found now to be erythromycin resistant. Note that the monoclonality means there were no resistant bacteria originally there in the population; all of the original, pre-mutagen bacteria were genetically identical.
When they investigated the penicllinase gene of the newly resistant bacterium, what they found was a single DNA base change, located at the site of the antibiotic binding pocket of penicillinase, which 'loosened' the pocket, allowing it to bind erthyromycin, which was then hydrolysed. This change somewhat lowered the activity towards penicillin, but a few more cycles of exposure to both antibiotics introduced another mutation which gave a 'better' pocket, as active as the original enzyme to penicillin, but able additionally to hydrolyse erthyromycin. The second mutation was located and identified.
The bacterium had clearly evolved a new functionality, without loss of the old one, by mutation and natural selection. There is no doubt the same change would have happened, albeit much more slowly, by natural mutation; there is no doubt the selection would have happened in the wild if the bug were exposed to two different antibiotics. Development of new antibiotic resistance in the wild is well-documented, and it follows the same pattern of point mutation as was described in this paper.
As it happens, it is likely most new functionalities don't follow this pattern; they more likely happen by gene duplication. Once you have two identical genes, one can mutate and go do something else, while the other maintains the original function.