Hi I checked out these links and particularly the Autosomal DNA Testing one as that is where my initial inquiry lay. That particular article is misleading through it's over simplification of how the average contribution from grandparents (and further back) any one given individual may actually hold within themselves as to actual genetic makeup. The really big factor in this is "crossover" or, more accurately put, natural DNA recombination that occurs when a cell spits into two functional selves. We all start off as a single cell (fertilized egg in the mother's body). For that fact alone, you will always be 50:50 your parent's contribution.
The real wildcard lay with what part of your parent's genetic makeup got saved to make you. Only half of their own specific genetic make up got saved to combine into viable cell which developed into you... with the rest discarded or not used (depending upon gender). Crossover occurs each and every time a cell divides during 'normal' cell division and is completely random in nature. By the time the a cell is destined to become either an egg or sperm, this has happened countless times... and only one of their own progeny goes on to result in a new human being. It is entirely random which specific bits of paired DNA exchange place and which combining sexual cells actually gets used to result in the baby. (The rest get's thrown out... a female's actual period is the result of discarding a fully ready sexual cell that 'could have become a person'). The same for any of a guy's unused sperm that does not goes on to do the same.
Of any given sample of a male's sperm, only eight will be identical. By nature's design, a fellow will produce a couple hundred million per ejaculation. A female will produce only several hundred viable eggs (nature design) and, at the very best, of these candidates only four will ever be identical. (She tosses out the other half, as she does not have the cellular resources to create the rest of the cellular 'machinery' needed for a full eight viable eggs that make for fully functional cell to operate when joined with the male's sperm/DNA contribution).
In any event, I have my answer here. Autosomal DNA testing can likely indeed identify a cousin, as the more matches there are the more likely this relationship as the result. However, it cannot identify with any degree of certainty whether or not the cousin lay within your parental or maternal lines. Crossover that occurs countless time between matched XX pairs before a cell results in a gamete prevent such a determination from happening. It is up to the researcher to figure this out (and hope that whatever he/she is proverbially making the decision from traits that are not commonly shared from both parental lines). Shared traits are common within groups sharing the same ethnicity - why they have similar.