Actually, and sadly, very few newspapers still have ombudsmen.
Although, what Sulzberger actually said was:
“Our followers on social media and our readers across the internet have come together to collectively serve as a modern watchdog, more vigilant and forceful than one person could ever be,” he wrote. “Our responsibility is to empower all of those watchdogs, and to listen to them, rather than to channel their voice through a single office.”
https://www.nytimes.com/2017/05/31/business/media/new-york-t...
"Our followers on social media and readers can be ignored a lot easier than a guy in our office, so when complaints come in, we can simply sweep them under the rug"
These days people get so worked up on social media anytime a brand does anything (i.e. people getting mad a cinnabon for their carrie fisher bun pic - http://cbsnews3.cbsistatic.com/hub/i/r/2016/12/27/a9c2ac0c-3...). I think social media can serve as a watchdog for more important issues, too.