Conveniently, this movie also never mentions that relevant fact.
Gray is a Nixon loyalist, and as his agents find an increasing number of connections between Watergate and the President, Gray gives in to political pressure and orders an end to the search.
The filmmakers totally skip over this revealing nugget of truth.
The record demonstrates that they acted not with criminal intent, but in the belief that they had grants of authority reaching to the highest levels of government.
His family was unaware that he was Deep Throat for many years.