To be fair, the "NYT" didn't lie - Broder did. The NYT backed up one of their journalists. Which they should!
WRONG. The editor should have read the article, said "You're full of shit" and rejected it.
You don't throw your soldiers out into the enemies tender mercies, just 'cause.
No, the NY TImes did not blindly defend Broder. The NY Times has a "Public Editor" - an independent source who investigates and publicly discusses whether the Times did the right thing on controversial stories. She's been looking into this controversy pretty closely - see her blog. She hasn't finished her investigation, but she does say "I reject Mr. Musk’s central contention that Mr. Broder’s Sunday piece was faked in order to sabotage the Model S or the electric-car industry."
Like any organization, the NY Times makes mistakes. But they have enough integrity to own up to it when they do.