If we were to go on just what we knew from The Invasion on through The Predator, we know there are Yeerks who bare ill will towards Visser Three. Iniss 226 flat out wishes the Council would demote or kill him in The Visitor. In The Messenger, the Yeerks find the Anis clothes and outwardly speculate that the "Andalite Bandits" may be human. One of the Yeerks in that group says, "Maybe, but I'm not telling Visser Three," or something to that effect.
So based on those bits of information, we know that Visser Three didn't exactly inspire loyalty and trust among his subordinates.
From The Capture onward we see numerous instances of treachery and subterfuge inside not only Visser Three's regime but the entire Yeerk Empire. It's not a stretch to believe that Visser One didn't have to twist arms to get a few of Visser Three's security personnel to look the other way.