Nothing to cite since I don't really go read those sites much anymore, at least for NFL stuff. I do recall it being mentioned when the pats lost to Denver (the hypothetical of all three being tied), but I really can't source that so I won't claim it as gospel.
I'm reading the rule differently than you are. You're as welcome to be as skeptical as my interpretation as I am of yours, or of trusting a beat writer to get it correct an hour after the game. Unless it actually comes to pass or an NFL official speaks to it, sorry, you're not going to change my opinion, as stubborn or incorrect as you may view it. It makes no sense to me that the primary tie breaker in almost any iteration is head to head but if it's three or more, you don't all have had to play each other - and YES, I realize it wouldn't make a difference - but the tie breaker steps are pretty convoluted to begin with, as witnessed by the fact this is even a conversation.
I'm perfectly willing to consider its poor wording on the NFLs part. But it could be poor wording on either end of that.
I really don't think it's that ambiguous: the only thing that suggests that NE wins the three-way is ESPN's Playoff Machine. I doubt an NFL official will ever speak to the actual tie-break rules - why would they if all the reports agree that Denver wins the three-way and there's no ambiguity? NFL.com's own
playoff scenarios generator has the Broncos winning the #1 seed in the event of a 3-way-tie between Denver, NE, and CIN. Even ESPN.com's
own view of playoff scenarios says that Denver clinches homefield if it wins and NE loses, suggesting that the fact that the Bengals can have the same 12-4 record is irrelevant. I was being facetious about Occam's Razor and ESPN earlier, but it really does seem like when every beat reporter and every other playoff seedings generator agrees on one thing and ESPN's Playoff Machine disagrees, the simplest explanation is that the machine was coded wrongly.
Also, while I can't seem to find a case of the 3-way-tie head-to-head tiebreaker actually coming into play in previous seasons, that tiebreaker was used to determine the playoff scenarios prior to week 17 in previous seasons. Here's an example based on last year's playoff scenarios: the Colts were 10-5, Steelers 10-5, and Broncos 11-4 by week 16 in 2014. If the Colts and Steelers had won and Broncos had lost in week 17, they would all be 11-5 with identical 9-3 conference records and all have the 2nd best record in the conference. And yet
Colts.com,
USA Today, and other sources stated definitively that the Colts could not clinch a bye in week 17 and were locked into the 4 seed (barring a tie between the Bengals and Steelers). Why? Even though those articles don't say it, you can reconstruct the logic and see that it was because Colts lost the head-to-head sweep and were 0-2 against Pittsburgh and Denver, even though the Steelers and Broncos never played each other. (Not enough common games - I think the Browns were their only common opponent.)