I believe you have it right as to the DNA evidence although it might have been that Meehan could not be excluded from one of the fragments, ie not a complete match. And it could have come from dander or other tiny cells that fell from him into a sample.
It may have been dander, which I think is a type of skin cell, but whatever it actually was, it was believed to be one cell. I don't know how full the match was but, as you say, he couldn't be excluded as the source of that cell, which puts the odds of it being someone else's well into the hundred millions is my guess.
My understanding in this area is quite limited, but I do know they're able to tell the difference between a cell that is a contaminant to an established sample versus a cell that partly or wholly constituted the original sample because of the way the samples are prepared before the extraction series for testing is done and the way they're prepared for retention after the extraction series is done. It should not happen, but identifying it (to a lab worker) is really more of a housekeeping measure so that all is accounted for. Contamination plays hell with juries, though, even though it doesn't degrade the original sample.