Yes, I have played a number of games with these same settings and I have almost always had 2 other civilizations in my starting sector, but I have never had one right next to me.

I exited the above game and started another one with the same settings and I did NOT get another civilization right next to me (at least I have not run into one yet), but I have encountered another undesirable issue.  I am only on the 4th month, but I have discovered 4 planets with a class of over 5 (i.e. worlds that could become Core worlds) and every one of them requires Extreme Colonization.  As can be seen in the Game Settings screen snapshot above, I set "Extreme Planets" to "Rare".  I do not think a reasonable person would consider discovering that the first 4 Class 5+ planets required Extreme Colonization to be "Rare".

I have to believe that there is something wrong with the logic for creating the initial layouts. 

I just started a new game in 77b - Mostly Abundant settings.  After 49 turns - 32 systems, 1 minor Civ, 10 no planets, 46 planets on other 21 systems (2.3/system) .  19 planets > size 15 (41%), 4 can be conlonized without additional tech.    Remaing 27 planets all 1-2-3- except 1 (5).  Does seem a tad skimpy at these settings, but certainly playable.

I maxed out the number of sectors as well and set Civilization Proximity to Far. I have four civilizations next to me in the same sector. That setting does absolutely nothing.