I don't buy the story about the historic reception of Sirius being red. As a physicist and a sceptic, I first would have to be convinced that the references are reliable. It would not be the first time that someone had made a mistake then it propagated through various generations, who simply copied the entries of target lists. You must realise that especially the Romans were not particularly skilled in Astronomy. If the report of Ptolemy is being considered a credible source for such a statement now, then contemporary poets, politicians and soldiers may have believed it as well without questioning. Note that even until the 17th century, astronomical "knowledge" was mainly deduced from philosophical tracts instead of empirical verification. "If Ptolemy said it is red, then it is red - even if I see it is blue."
Today, it is very difficult to judge, why this idea came up. A true change in colour would be the last reason, I'd believe in.
Nevertheless, since the companion is a white dwarf: there is a class of binary stars -
cataclysmic binaries - in which the orbit of the companion is so close to the primary host star that matter is transferred and accumulated onto the white dwarf. As soon as a critical mass is accumulated, a runaway reaction produces an outburst (a nova, or supernova Type Ia). But then, we nowadays should be able to observe a remnant of such an outburst, which apparently we don't in the case of Sirius.