The initial justification was a combination of things, presumed 8:11 jump time, radar at 8:11, recording of the sound of the pressure bump, comments of - lights of Portland on the horizon, last point of contact at 8:05, estimate of oscillations a few minutes after last contact, wind direction and speed, estimates of canopy drift within pull ranges.
I think the search was based on sound judgment at the time. Part of this is also show: this event captivated an audience and the response is to signal an overwhelming effort to help reinforce a low perception of success and reinforce deterrence.
Deterrence is the primary objective of law. Investigation is secondary - the reactive element of the law when deterrence has failed. Prosecution/sentencing are tertiary and used to restore deterrence by reinforcing consequences and signaling a low probability of success to would be criminals.
The search whether sound or not was necessary.