Just speaking as an attorney, it really wouldn't surprise me if NBC's lawyers told them to sit on the tape for a few days to go over their legal options/risks. It's what us lawyers do. I doubt there was any malice involved either way.
Stop bringing logic into this. It's obvious that the only reason anyone would ever wait to air something is because they never planned to air it at all.
For what it's worth, the NY Times and Washington Post editors went on record a few weeks ago saying they would risk jail time publishing Trump's tax returns. To them, I doubt this tape was that much different.
NY Times, Washington Post editors: We'd risk jail to publish Trump's tax returns
"Some things you have to do," said Woodward. "Dean is exactly right. This defines Donald Trump."
It's only hypothetical but I can't imagine the Presidents of NBC or NBC News saying that.