This is what makes this no better than any other VPN service. I still need to completely trust that the provider is not watching me. Even with full hardware access, there could be an invisible sandbox or hardware DMA to some chip I can't see. There is no easy scalable solution to avoid this in a technical level. But you can be one anonymous user in a sea of many others and hope for the best, which is why I'd advise to go to a trusted mainstream VPN provider.
And with root access to the VPS host, you can just extract private keys from the VPS ram and proxy the connection, logging it all the while..
so no, this claim is not tenable even at the VPS level.