Nothing wrong with the idea of a black hole sucking in mass, but if it were sucking in that much mass, say on the order of 1-10 stellar masses every billion years, it would be very bright in the x-ray spectrum. I don't think this one is exceptionally bright or that is the first thing they would have thought of.
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.
OK, scenario 2. There are two moderately (but not extremely) large stars in close proximity. One of the stars, in technical terms, goes blewey, and leaves a typical black hole remnant. The outer atmosphere of the second star is disrupted by the blast, and much of it remains gravitationally bound to the system. Some ten solar masses or so of the companion's ejecta are eventually captured by the black hole; the rest eventually falls back to the companion star.