Did we get closer to another plane than we were supposed to, or was the pilot just protecting our delicate sensibilities? Yesterday, April 28, 2019, I was flying on Alaska flight 557 from LAX to PDX.

About an hour into the flight (near the California/Oregon border) I was looking out the window and saw a jet travelling the opposite direction from us.  It was travelling exactly the opposite direction of us and I saw it when it was ~45-60 degrees forward of us.

Within a couple of seconds of my seeing it, we banked sharply to the right.  It was not a violent turn; An answer to this question describes true evasive maneuvers as, "those of you not strapped down would have been hurled to the ceiling or slammed to the floor and your stomach would be heaving in a different direction from the rest of you." - and we didn't have anything like that.  I'm not sure I would have even noticed the turn had I not been looking out the window.

However, it was a pretty sharp mid-flight maneuver, and because I was over the wing, I didn't get to see the other airplane at closest approach because the wing blocked my view.  I would estimate that it was about 3-5000 feet away from us.  I felt like he was at pretty close to our altitude, but again, as the linked question says, that's hard to say for sure.

The linked question points out that distances and altitude differences are hard to judge.  That's fair, so I'll offer the following bona fides:


I live about half a mile from a commercial airport, perpendicular to the end of the runway, so I have a good idea of what jets that are half a mile away from me look like.  I would estimate that the other jet was a bit but not a lot further away than that. 
If two jets pass by each other at 1/2 mile, and you can see another jet that is 60 degrees in front of or behind you, and he, like us, was travelling 480 mph, he would have been in my field of vision for 6.5 seconds.  That sounds about like what I remember.  At 3 miles, that number turns into 40 seconds.  I don't remember the exact amount of time, but my initial estimate before I did this math was 8 seconds.  


I could imagine our pilot banking the plane simply to lessen the odds of the passengers noticing a safe encounter, as even a safe encounter leads to awkward questions on sites like this.  

So, my question: Did we have a near miss, or was this a standard close-but-intended encounter?
From the flightradar24 playback, it appears to have been an encounter with Etihad Airways 171. 

Your flight (Alaska) was at FL360, while the opposing was at FL370. Therefore, there was 1000 feet of vertical separation between them, which is typically considered safe when operating with RVSM, Reduced Vertical Separation Minima rules (see other answers).



I also looked up the LiveATC recordings archive (Seattle Centre Sector 14 high, 28/04 2000Z), and found a clip that I think corresponds to the event:


  
  Alaska 557, can we take a heading right of course to avoid some wind?
  Affirmative
  Ok, deviation approved [...]