Is the NFL making up rules as they go?

Let me start by saying I’m not a huge football fan, and couldn’t really tell you the last time I watched a full game, so it may be that the rules have changed since the last time I watched, but there was a play in yesterday’s playoff game that bothered me. Cincinnati had just completed a pass with 13 seconds to go in the first half, and the player was pushed out of bounds. The QB took a quick snap and spiked the ball, leaving 2 seconds on the clock. The referees then reviewed the previous play. Even though Cincinnati scored a field goal, and the end result is likely to have not changed, my issue is three-fold. First, should the receiver going out of bounds have stopped the clock? Last time I watched a full game, it would have. Second, barring that, shouldn’t have the clock stopped, at least momentarily, while the chains were moved? And finally, and, I think, most importantly, the last time I checked, a play could not be reviewed if another play was run in the interim. Did the referees review the play in violation of NFL rules? Or did that rule only pertain to challenges, and not reviews initiated by the officials?

The end result of this is that the play stood, Cincinnati scored, but lost the game, and nothing would have likely changed. Just curious as to whether I missed a rule change since the last time I watched or not…

Update: According to the 2013 NFL rules posted online (Section 9, Article 2, Note 2) “The Replay Official must initiate a review before the ball is next legally put in play,” so it does, indeed, appear that the officials were making stuff up as they went.