To get anywhere at this point in the serial, the Doctor needs to find a reasonable person who hasn’t already made up his or her mind about what’s going on.
Yeah, good luck with that, Doctor.
So, what do you do when you’re arrested and accused of being a spy in a war you’ve only just heard of? If you’re Jo, you try panicking and coming up with impractical plans. If you’re the Doctor, you have a good sit down and wait to meet that aforementioned reasonable person who will listen to what you have to say, let you go, and maybe help you find the stolen TARDIS. Heck, even the threat of a mind probe doesn’t mean much since the Doctor isn’t lying, so there’s no reason to worry. They just need to wait for that reasonable person.
And sure, the woman President of Earth might be inclined to listen, but one General Williams believes Jo and the Doctor are spies for the Draconians.
And the Draconian prince? He believes they might be spies for the humans.
Yeah, this isn’t going very well.
Now, the Doctor realizes that someone is trying to start a war, but he doesn’t quite know who, and when the Draconians decide to steal Jo and the Doctor from custody, things get worse when the Ogrons show up to capture the Doctor.
Jo? She got to the human government, and General Williams still thinks she’s a spy.
This is not going well.