In the game jobefunhouse017, I play as the Xenos with my Planetary Institute already built, without having the tech tile that makes big buildings worth 4 power points. The game allows me to make the following federation with 7 satellites (indeed, this is the only suggested location for a federation):
However, when choosing a custom location, I can make this federation with only 6 satellites:
If I understand the rules correctly (as posted on https://boardgamegeek.com/thread/2120375/official-federation-faq, to which you also link when creating a new GP game), I should only be allowed to create the second federation with 6 satellites. From that thread:
Q: The path with the fewest satellites to link my chosen planets will touch a planet that I did not wish to include in my federation, can I choose the shortest path that skips this planet? A: No, If the "extra" planet cluster is not already a part of a federation, then you must choose the path with the fewest satellites to link your planets, even if it includes extra planets, this is typically where the third rule can come into play making that federation invalid.
Q: While choosing the path with the fewest satellites to link my chosen planets, I notice that I can use fewer satellites by using a planet cluster I did not choose to be a part of my federation as a "hop" to cut out 1 or more satellites, Must I use this path? A: Yes. The path with the fewest satellites MUST be used even if it is achieved by using a planet cluster as a hop to avoid using more satellites.
Note that in both cases, I didn't end my turn, as I don't want any of those federations at this point, so maybe another check will stop the first federation. However, a check is performed after choosing a fed tile, and that check allows both federations, but not an unnecessarily big one with e.g. 9 satallites.