Rule 1 is aimed at other archetypes besides the Synthesist. It also bans the Evolutionist archetype as well.Alright, this is just for future reference for anyone who may come across this thread in the future, I found this post entry, made by John Compton, Pathfinder Society Lead Developer on a thread concerning the Shaitan Binder archetype for the Unchained Summoner in PFS.
After reading it, I am still scratching my head on this and don't know what to fully think of it. After reading it the only two concrete things I can say on the whole debate we have had in this thread are:
1. The rule: unchained summoner qualifies for all existing summoner archetypes, save those that modify the eidolon's type or base form only applies in PFS organized play.
2. The Synthesist archetype is banned in PFS no matter which version of the summoner you use for your PC. Making the above rule kinda of moot.
Sorry I edited the number 2 part of the post because I meant to say the Synthesist being banned makes the whole modify base form argument for Synethiest kinda of moot for the whole thread debate. The post I mentioned is what I was looking for when it came to the clarification of the unchained Society ruling on Summoner archetypes.