Parity does not run on the EVM, it's a local node processing a local copy of the blockchain. You can create normal accounts which are just private/public keypairs you have full control of without anything "being in the cloud" or "distributed". What you are referring to might be the vulnerable multi-signature wallet itself, which - once deployed - runs on the EVM. And that only affects a fraction of Parity users.

Note, I work for Parity.