Do you not understand how parenthetical statements work?
The parenthetical statement about saving throws is an explanation of what they mean by the fact that mindless creatures are less likely to find something unbelievable.
In a hypothetical situation, in which you cast Silent Image to create an Illusory wall in front of an enemy, a mindful creature is capable of saying, "He could have summoned a wall, or he could have cast an illusion." And thus be likely to test the solidity of the wall.
A Mindless creature, depending on it's orders might on the other hand just stop moving (if ordered to attack nearest visible creature) or decide to pummel the wall thus getting a saving throw, if ordered to directly attack most recently located enemies within a certain area, or maybe it might look for a way around the wall if it has been ordered to seek out enemies that attempt to escape.
Yes, WotC writers thought for some strange reason that minful creatures could get saving throws without interacting or studying, when they cannot. But it doesn't change the fact that they clearly explained that Mindless creatures are less capable of discerning illusions as illusions.
I am frankly boggled by how you could even get the conclusion you did from any part of that passage, even out of context.