Easily.
The Milky Way looks more or less like this when viewed from outside it.
The bright center visible in the middle is in the range of 5,000–10,000 light-years.
The supermassive black hole roaring right in the middle is less than 0.000005 light years in diameter (2.6 light minutes).
The effect of that black hole on the brightness in the middle is practically the same as coloring 1/0.00000015 pixels in the middle of that image black. Yes, the black dot is there in the middle, but we can't see it because there's so much bright stuff around it.
It's a bit like taking a damn big spotlight, plugging it in and turning it on, looking straight at it and a guy dropping a grain of sand into the spotlight - the grain of sand is there and covering part of the spotlight's beam, but you just can't notice its effect. and we can say that the spotlight is bright.
edit:
You almost forgot to mention that even though nothing, not even light, can escape a black hole, its immediate surroundings are still shockingly bright, as the gas/matter falling in gets really hot and it looks something like this - there could be a roughly 10 light-minute area around the black hole: