I think it depends. If someone just stays on welfare without seeking jobs or something (by their choice) then I think people will think they're poor by choice. But I don't think I've met people who thought poor working people were poor by choice.
I've met a few people like that. The logic is that poor working people just aren't applying themselves enough, and are staying in their low paying job by choice or lack of motivation to skill-up and hustle for a better paying job.