Can matter fly directly into a black hole and avoid the accretion disc? From what my non-scientifically-trained mind understands, matter typically enters a black hole via getting caught up in the accretion disc going faster and closer to the black hole until it passes the event horizon, the point of no return. Using Earth as an analogy for a black hole, I assume the accretion disc would orbit around the equator, similar to Saturn's rings, and the matter might eventually crash into Brazil or somewhere along the equator?

My main question is, can matter simply do a straight shot into the black hole at a higher latitude, say straight into New York City, avoiding the disc altogether?

As you can probably tell by my simplistic analogy, I am a complete layperson. While fancy jargon and artistic looking equations might be expected (which is fine), please also dumb it down to an average intelligent business administration major's level of scientific understanding.
In your analogy: A satellite stays in orbit because it has angular momentum. This always balances the force of gravity, thus when being in the satellite (or in the ISS) it seems as if you're weightless, because force balance. This is very important to understand, because it is the reason that in space all orbital motions can -in principle- go on forever. Because angular momentum is conserved.

Now in order to crash into the Earth/BH you need to have very low angular momentum (which is equivalent to having only linear momentum straight down into the BH) or you have to loose the angular momentum somehow.
Near Earth, this happens to the ISS, because it has a low-earth-orbit between 350-450 km and at this height there are still enough atmospheric particles around to produce drag.  

Around black holes it is a very similar thing.
I will define the Schwarzschild-radius $R_s = \frac{GM}{c^2}$ as a relevant length-scale. Then, as long as we are outside $3 R_s$ distance from the BH, we need, as on Earth, friction to dissipate our angular momentum. In the case of accretion discs that form around BH's this can be accomplished through turbulent dissipation as laid out in the famous paper by Shakura and Sunyaev.  

Then, only very close to the BH, namely at a distance $&lt; 3R_s$, space-time distortions help us to fall into the BH without the need for any additional source of friction. As you see, this is a region very close to the Black Hole and it is misrepresented in popular accounts of BHs that all matter orbiting it will magically fall into it.