He would have been neglecting to do his job. You can’t assume something would have been off the record: either it is clearly established as “off the record” (or on background or something else), or it’s on the record.
The fact that this is journalistically right overweighs the issue of “real” wrong, in my opinion. In real life, it’s nosy. It’s not so nosy when that’s the job.
It hits me as naive and unwise on your part.
Well, yeah. That’s what I said.
-FrL-
Why? 
Because the evidence is that the dude hates you. Why would you disregard it just because he didn’t know you would hear him?
I didn’t say I would disregard it. I said I would not hold it against him.
Analogously, I’m not saying the Journalist should have disregarded what he heard. I’m just saying he shouldn’t have reported it. (Though see my post above where I give an argument against myself on this point.)
-FrL-
What’s the difference?
How is this analogous to reporting such a statement?
We’re talking ethics here, right? What are the ethics of “holding something against somebody”?
An analogous situation would be for you to tell someone else, “I overheard the dude say he hates me.” That’s not unethical, even if you’re not engaging in journalism.
Confronting him with it would be a bad idea, but ignoring it would not be smart.
The distinction you’re making here, both with this analogy and with regard to journalism, really doesn’t make sense. The journalist’s job is to produce a report of what he’s learned. If he doesn’t report what he heard, that’s the same as disregarding it.
It’s worth noting here that there are uses for “off the record” information. For example, if someone tells you something valuable and says you can’t print it, you can take it to other sources and get it confirmed elsewhere. That way your first source stays off the record but you have printed and confirmed the information.
The flip-side question seems interesting as well: Is Dougherty obliged to report Moyle’s comment? It seems to me that from Dougherty’s point of view, the practical analysis is largely the same as if there had been prior agreement to be off the record. In either case, the reporter has to consider, “if I print this comment that I’ve been asked not to print, my source may stop talking to me.” (Certainly, if there’s a previous agreement, that ups the ante, but the basic analysis doesn’t change.)
So can Dougherty legitimately opt not to print Moyle’s and Smith’s remarks, even if he deems them newsworthy?
You do a cost-benefit analysis in that case, and it involves some personal knowledge of your source. Again, I want to note that “you didn’t hear that” isn’t the same as “that’s off the record.” Depending on what the source is like as a person, it could mean anything from “we’re through if you print that” to “I know you’re going to print that and I wish you hadn’t heard it.” If Smith is a regular and reliable source, you may not want to alienate her. If you’ve never seen her before and probably never will again, that’s not such a big concern. I don’t mean to suggest journalists are heartless, but it’s not a requirement that every source who ever worked with you is going to be happy with you and what you wrote.
The argument for not printing sounds pretty weak, in this case. The topic of the article is voter registrations in the county and how they’ve shifted dramatically. A lawsuit challenging those registration is important, and you can see Dougherty put it in his fifth paragraph.
I think it’s also noteable that Dougherty reported that he was asked (after the fact) not to report what he’d heard.
As a reporter, what’s said in front of me is fair game. A source can request to go off the record – before the fact, as said above – but there is no guarantee that that information won’t see the front page. The reporter will often use what the first source gave to formulate questions to other sources. This is usually the reason for giving off-the-record information, in my experience.
It is bad form to insinuate yourself into a news story. He could have just said that the conversation took place, and then thrown in Moyle’s later comments. Reporting that it was asked to be off the record is also (imho) bad form. It is unnecessary unless the story is about a coverup (which I didn’t see in this story), and it exposes the reporter’s bias. It seems like an intentional dig, and the reporter may have burned a bridge that was still worthy of repair.