- She can't be worried about the prospect of being strong-armed into being Deanna's nanny AND some refugee in a war-zone at the same time.
- Worrying about being shoved in a dungeon means that she's a heartless monster who doesn't care about the refugee in the war zone.
- If, by some miracle, she saved the refugee in the war zone, she'd agree that having to deal with a family that's proven its active hostility towards her and smugly resists any attempt at fair treatment is a minor thing in comparison.
The reason that this rather vile technique works is that the jackass doing so manages to bully a hapless opponent into silence because she doesn't want to be accused of not caring about refugees in war zones.
The sad thing is something I'd mentioned earlier: April wasn't the first to have to listen to that sort of hateful bullshit. I remember one strip in which John told Liz to either quit feeling bad about her appearance or go to her room; her attempt at gaining his sympathy was met with his blathering about refugees in war zones as well. As would happen later, her complaint was silenced by the logical fallacy that worrying about being cruelly mocked either conflicted with worrying about worse things or made her a bad person or something. It's a cheap, nasty way of avoiding to have to reassure someone that you don't actually care about.