ECC can be used to encrypt the data itself with the public key instead of encrypting a random key and then symmetrically encrypting the data with that random key. But this is not a good idea as explained in [Thomas Pornin's answer](https://security.stackexchange.com/a/20145/12216) to https://security.stackexchange.com/questions/20134/in-pgp-why-not-just-encrypt-message-with-recipients-public-key-why-the-meta-e.

In any case [ECIES](http://en.wikipedia.org/wiki/ECIES) uses a symmetric encryption algorithm to actually encrypt the data, so even if you use ECC to encrypt all the data, you're still encrypting it with a random symmetric key. But if you're encrypting the data itself with ECIES you could use a simple XOR as the symmetric encryption algorithm, which is effectively a one-time-pad. This has a theoretical advantage in that, unlike other symmetric encryption algorithms, one-time-pads are information-theoretically secure.