In a far off future, where enough DNA data is publicly (!) available, that may be the case. Until then, to which data set should any company compare my DNA to find out who I am?
23andme is collecting data at a fair rate, there are other companies like them. Pooling the data between all those companies is going to allow you to fill in a bunch of 'blanks'. At some point that will reach critical mass and you can map the remainder.
I'm not good enough at math to give you the percentage of a certain population in order to be able to infer the rest, maybe someone else here can do that.
But given a population size 'n' if you get a random distribution of individuals and you know their genes and you know have a graph of relationships (say through facebook or some other means of tracing links between people) you should be able to make a formula that tells you what kind of 'coverage' you can expect based on how large a sample.
