Almost. RAND() writes the rand seed as meta data to the binary log. It's safe (as is NOW() - like you pointed out). UUID() is not safe though. But examples

Almost. RAND() writes the rand seed as meta data to the binary log. It's safe (as is NOW() - like you pointed out). UUID() is not safe though. But examples like this are so special case - it doesn't show the real danger. A DELETE with a LIMIT clause and no ORDER BY can semantically delete different rows on the slave than on the master. You never, EVER want to use circular replication (A->B->C->A). Surrounding a crash it's such a pain to re-piece together the data.