No, Chromium is FOSS and every compay or dev is free to modify it to their like. Do you think that Windows with EDGE follow the rules of Google in this Chromium? Or the Chinese Opera? Vivaldi also don’t with its gutted Chromium, But Mozilla does, even with Google devs working on Firefox, because Google is its major sponsor. Sends Data to Alphabet and Google analytics, because Mozilla made the mistake of making a contract with the devil, losing independence by relying on outside investors, above the worst one.
I know that the Firefox fanboys are going to pepper me with downvotes now, because life is hard and so is the truth. The enemy is Google not the engine. Chromium folds to Google only if you use it as-is, without bothering to remove the GoogleAPIs it contains by default.