Right, they pretend it's parallel when in fact it's serial. The first illegal search is what generates the lead, no matter what secret rationale they come up with.
NSA surveillance of a smuggler in Mexico produces the name of Joe Schmoe in El Paso (for concreteness let's say the intercept is "Joe Schmoe will distribute our cocaine, as always"). The DEA gets tipped, Joe Schmoe's name goes up on a tack board and he's put under surveillance. A case may be built from there using classical police methods.
