Last year we decided to move to my home country because of "too many things" but also fed up of feeling an immigrant.
Few months ago I met a German family living around here in a coastal area. I asked them why they moved here and they answered me straight to my face "Because in Germany there are too many immigrants". I think the joke tells itself.
In general, you can totally be against the way immigration is handled in one place while being an immigrant elsewhere.
The family you mentioned likely considered themselves different from the immigrants that they complained about.
I'm not agreeing/disagreeing with these people I don't know, but the general point is fair.
This reminds me of those UK elderly living out their pensions in Spain voting for Brexit to reduce immigration. Thanks to outrage media, I think this public perception of immigration ruining everything is almost everywhere now.