The fact that the companion star is feeding the black hole suggests that it is filling its own Roche lobe. As the black hole grows, the Roche lobe of the companion star is going to shrink, which means that more of the star will be available to the black hole. Over time a significant fraction of the star migrates to the black hole.
Anything obviously wrong with that model?
(I still don't understand the peculiar sentence in the article, BTW.)
Then there is the theory that it swallowed another star in a short time billions of years ago, leaving no observable trace today. That would be improbable because it would require the star it collided with to be lined up almost perfectly, otherwise the best it could do would be to capture the other star into a decaying orbit and eat it more slowly.
I wish I were an astrophysicist with the training and computer models to play around with -- this is fascinating stuff. Getting someone to pay for this type of research is the hard part, maybe even harder than doing the research IMHO.