Days after a blockbuster video emerged capturing Donald J. Trump, then a reality television host, making vulgar remarks about aggressively kissing and groping women, a question was still reverberating around media and political circles:

Why was NBC not the first to report its own story?

The footage of Mr. Trump came from a 2005 segment for “Access Hollywood,” the syndicated entertainment program owned by NBCUniversal. The video was discovered last Monday by an “Access Hollywood” producer, and Andrew Lack, the chairman of NBC News, learned of the tape’s existence the next day, according to two people briefed on internal network discussions.

Yet on Friday afternoon, it was The Washington Post that posted the video to its website, rocking the political world and earning the envy of journalists across the country.

The delay stemmed from a combination of factors, including a legal review, intranet work fiefs and the slow-turning wheels of a sprawling corporate infrastructure, according to several people familiar with the process, who spoke on the condition of anonymity because of the sensitivity of the internal discussions.

The Post reporter who obtained the tape, David Fahrenthold, received a copy late Friday morning. When NBC’s news division learned that The Post was working on the story, it moved quickly: Within about 10 minutes of The Post’s publishing its version, the NBC News correspondent Katy Tur went on MSNBC with a story about the video, showing the footage.