On computing the number of independent values from a signal's bandwidth?
It comes from the Nyquist rate.  The Nyquist sample rate for a signal with bandwidth $B$ is $2B$.  In other words, that is the lowest sample rate that will contain all of the information in the signal without distorting it (i.e. without losing information).

The question implicitly assumes that the sample rate is $2B$, and thus that in time $T$ you will get $2B*T$ independent samples.  If the sample rate was greater than $2B$, then the signal would not be "white" anymore and the samples would have some correlation.