If you read the study at the link, you’ll see it’s sloppily done and poorly designed. The study used a tiny sample of medical students (488 out of >80,000 US medical students) who responded to 5 questions. Familial pressure AND having family members who were physicians were conflated into a single question.
Also note the study was conducted by a for-profit HR company fishing for clients.
I won't deny that upper middle income applicants are advantaged in the admission process because they are better able to amass the necessary ECs expected by med schools, have better academic preparation (starting from elementary school onward so they tend to perform better in college), and are more able to afford the expensive admission process (including prep classes for the MCAT), but I doubt there is any conscious bias against lower income applicants.