A CNAME record points your subdomain (e.g., blog.example.com) to a SaaS provider (medium.com/@brand). While this works for users, search engines may give SEO credit to the SaaS provider instead of your domain.
A reverse proxy, on the other hand, fetches content from the SaaS provider and serves it under your domain. To Google and other search engines, the content belongs to you — boosting your domain authority and rankings.
See how to set up a reverse proxy here - https://publicityport.com/awc/5552/how-set-reverse-proxy-replace-cname-nginx-apache-cloudflare