Eric, what you said was that I was incorrect for stating I used an AND gate to acheive a low output when any givien input goes low. By the definitions I've read of an AND gate, that's what exactly I should be using. Additionaly, it works.

The datasheet for the thing calls it an AND gate. I found it by searching for an AND gate. I bought it due to its being marketed as an AND gate. And it works as an AND gate.
You know, that's about the only part of this project that I haven't been (too)confused about.
And as for whether I'll "never get that result from an AND", well,
That's exactly the result I'm getting.
That being said, you were right about this:
"I guess that the direct connection has result b) and the negative OR has result a) "
I didn't know that a pin's output configuration would have anything to do with its behavior as an input. I tried configuring the column outputs as open-drain, but they presumably aren't able to go "High enough" to work with column scanning method. I assume this has something to do with pull-up resistance.
Keep in mind, that this is my first attempt at working with ANY kind of micro, writing code, or anything. I'm learning everything as I go, so I'm sure some of my questions and problems seem elementary to most forum users here.
So thanks for the help.