Refugees aren't immigrants. You can have fully closed borders on lockdown and still take in Refugees, it's a completely separate political issue from borders.
The problem with the refugees is that taking them in basically mean you side with whatever side they were on when they fled and since they fled, they are obviously losing so governments are REALLY hesitant to throw in their lots with the losing side unless their own interest is already at risks. AKA Politicians are cowards who don't give a shit about helping anyone no matter what.
I mean that's the point in the story, it's SUPPOSED to be annoying and stop the MC from making any actual point because she'd just slaughter him, he can only win by throwing platitudes and stopping her from talking.