Does Metamask not really know what tokens I own?

This 60-second clip claims that Metamask does not really know which tokens I own:

https://youtube.com/clip/UgkxSTDXnku5O8ldTXPz179wparSMPSMeYlh

It also suggests that I don't really 'control' the tokens but that they are in control of a third party smart contract which basically I have to trust to make good on a liability to me.

It suggests it is not due to Metamask, since the Ethereum network also cannot know which tokens I own, but has to rely on 3rd party smart contracts to tell the truth.

Crypto appeals to me since because of full control and ownership, but this suggests otherwise.

So, is this true and how can it be fixed?

-- Update after 24 hours --

Thank you all for the informative replies below. From what I gather it looks like Metamask is doing what it can and that user tokens reside as an IOU within 3rd party smart contracts. An alternative network paradigm could be that tokens are native to the blockchain and the network is trusted with taking care of storing and transferring tokens, so that a hack or a bug of a 3rd party smart contract does not immediately effect your possessions. Of course you'd still have to trust the network, but that trust is the prerequisite for crypto in the first place. Anyway, it seems from the debate below that people pro and con network native assets / tokens are balancing out, I am thinking of setting up a poll.