Yes, we can, indeed, "see" a black hole and we just did not too long ago.
You see, being able to "see" an object is not solely about "reflection" alone: rather, you "see" things by them interacting in any way with the light that reaches your eye (or other "seeing" instrument), and then by your eye interacting with that object-interacted radiation. Reflection is just one way. Absorption (the removal of light rays that would otherwise reach your eye) is another, and you don't need a black hole for that: any object that is not totally transparent, shiny, or white, under white light, must have absorbed some radiation for it to look that way.
If you took a big ball and painted it black and hung it in front of a light background, would you say you were "seeing" that black ball? If so, that is not very much different. If you agree you can "see" that, then you can "see" a black hole, just same. It does the same thing: it absorbs the light from any luminous background, distinguishing itself because those rays that were sent from the points on the background you'd see were it not there, fail to reach your eye. Likewise, if you want to argue you "cannot 'see'" the black hole, then you cannot "see" that black ball either, by the same reasoning.
Now, of course, the mechanism of the absorption is different in each case, but the result is the same in terms of what happens to light rays. Rays that would have been otherwise able to reach your eyes (or here, cameras) were the object not there, now don't.
You also mention that the picture is "colorized". This is true, but it's not because black holes "can't be seen", but rather because that the telescope is "seeing" in a different wavelength range than your eyes do and that's because those wavelengths have advantages for detecting them at this level of resolution and at this distance compared to visible light, not because that we could not see the black hole with our own eyes were we there (and suitably protected from the intense energy). Colors are always arbitrary, being assigned by our brains. Light itself doesn't have "colors". Since our eyes, and so our brains, aren't set up with (kind of tautologically) receptors and hence color channels for wavelengths we can't see, we've got to reuse the ones we've got somehow. This doesn't make it any less a "real photograph" though, any more than taking a greyscale photograph of a scene with an ordinary visible-light camera does (and if anything, I'd have put it in grey, but I suspect the red is because they want to make it look "fiery", so it's a little artistic license.).