Endless Space – Why Don’t Industry Conversion Techs Work

Once a faction has the off string travel, it can travel through any territory, regardless of treaty status, to reach its destination, so long as it is traveling off-string. In your posted example picture, the Ameobas are traveling "off-string".

There was a bug in the game that allowed anyone to travel on-string regardless of treaty status as long as the destination was an unexplored star.

I'm not entirely sure how you ordered your fleets, so I'll throw a bunch of fleet movement facts out and see if any resonate.

First, on travel speeds: String Travel (blue arrow number) is usually the fastest means of travel. It's possible that you've done research such that your Direct Travel speed is so much higher that your String Travel speed that this path is actually shorter.

Usually the situation is inverted and the String Travel is the "scenic" route, so my usual calculus got really tripped up by the picture. Herp and derp. In those situations, it's possible that the scenic route will be travelled more quickly than the "direct" intersystem travel (green arrow number), despite the longer distance. Your ship actually figures out the fastest path to its goal when you give it a movement order, so in that case the string path was faster. Paths can have a mix of Strings, Direct Travel, and Wormholes, depending on the geography of the galaxy.

Second, on orders: As noted, you can force Interstellar travel with Ctrl + Right Click, in case you want to bypass a particular system (such as flitting around a fleet too large to engage or opening new fronts). Direct Travel also allows one to pass through Influence borders, the colored auras emanating from planets, unlike String Travel. Certain diplomatic situations cause Influence to act as an impenetrable String Travel barrier. You can string together orders with Shift + Right Click, so you could have manually created the order to move in such a way with Ctrl + Right Click on Ita, Shift + Ctrl + Right Click on Quyos.

Conclusion: Excluding the research possibility and excluding that you did this manually and forgot about it, the pathing would seem inefficient.