mining pools – What does verifying a fake transaction mean?

The tweet seems very confused. Most likely, they meant “60% of the hashrate” rather than supply. It’s not clear from the tweet what they mean with “verify a fake transaction”. Charitably, one might interpret that they could execute a Finney attack, or execute a doublespend attack by reorganizing the chaintip in a form of majority attack. As written, it rather does sound as if the author of the tweet thought that miners could include invalid data in their blocks and the network would go along with it, which would imply that the tweet’s author did not understand that all full nodes on the network independently verify blocks and reject invalid data.