I see this phrase everywhere. Isn't it a pointless statement? Is it not equivalent to "Trademarks are owned by their owners"?
The purpose of such a statement is to disavow the reading of any impression that the person making the statement is affiliated with the trademark owner, because the gravamen of a trademark infringement suit is that the person using the trademark mislead a consumer into thinking that the person using the trademark was endorsed by or affiliated with the trademark owner.
The purpose of the statement is to make sure it is clearly understood that the person making the statement is not affiliated with the trademark owner and not in any way trying to insinuate that there is an association. It's an effort to avoid an infringement suit by giving proper ownership credit to the owner of the trademark itself.
You can liken it to a belt and suspenders approach, but more stylish.