If DNA cousins and I share the exact same segment of DNA, does it always mean we're related via the same side of the family?
Background: I have taken DNA tests with National Geographic, Ancestry, and 23&me. I really like the more complete, detailed information 23 provides. So, in an attempt to more fully understand my DNA and figure out shared lineage with cousins (whether I'm related to them via my father or mother's side, and perhaps even trace to which exact great or greats), I started a spreadsheet. On it, I have rows for each DNA strand (1-22, plus x) and columns for segments starting from the lowest numeral (1) to the highest, dividing them up in between according to clusters of shared DNA numbers I share with various cousins. Under each strand, I have a row for each cousin. The result is that I have found multiple cousins who line up in the same column because they share the same exact segment length (e.g., 1-5,679,900) for a particular strand. If I am able to connect with one of those cousins and figure out exactly how we're related (usually by using Ancestry trees), I conclude that I'm related via the same ancestor(s) to everyone else who shares those specific segments.
Then it occurred to me that my thinking might be completely off, since I'm so confused about DNA. Because half of each segment comes from the maternal side and half from the paternal side (I think), then my spreadsheet is worthless. Or is it? Please advise.