Also, there are other aspects to hashkafa besides “involvement in the secular world” so they may consider themselves to be hashkafically Chareidi in other ways.
I guess the main point is that if their Rabbanim are Chareidi and they are sending their kids to Chareidi schools, they clearly feel that Chareidi hashkafa is the ideal even if they find it hard to live up to that ideal (whether in their actions or their hashkafos). I do have the impression that this is a common phenomenon in Brooklyn.
I’m curious what England is like since you mentioned that you never heard of this concept before? Are there people who would fit this description? I feel like I have met people from England who seemed to fit this description more of less, but I’m not sure.