A deleted tweet from last month which could explain the current pump?
From the news and different articles that I read, it appears that the current pump that we are seeing right now is due to the airdrop that has been scheduled to be given to those who hold ETC in their wallets. We already experienced this kind of pump with this same coin when it facilitated its first airdrop few months back. Take note that after the airdrop, the price of it crashed hard as people sold their ETC after receiving the free token. So expect the same thing will happen again.
To comment on the screenshot that you provided, I think it is impossible right now. Coinbase didn't support the ETC chain last year and I think they will not change their mind now. Don't make something big out of that tweet. Well, if it is indeed true, then ETC will soar even higher in the coming days.