That's one way in which crypto is different from every other asset. The ownership relies on cryptography, not law.

Legal ownership is one of the a weakest forms of ownership. A step above that is physical ownership (e.g. gold stored in a secret vault). Cryptographic ownership is even stronger than physical ownership because nobody can take it away from you unless you tell them that you own the thing to begin with and then you willingly give them the passphrase or transfer the tokens.