The Eve JazzO is referring to would be the UrMother of all the humans on earth in strict matrilineal lineage.

Yes, somewhat, but it's not saying that there at one point existed only one woman on earth who begat everyone, just that the genetic bottleneck resulted in only her mitochondrial DNA passing on. There's also evidence of a common male ancestor based on the y chromosome, but he's not dated to the same time period as "Eve". It would have been a different bottleneck at some other time.