False. You and anybody can sing and record any currently published song without asking anybody’s permission. Go ahead and record yourself singing ‘Hey Jude’, upload it to iTunes and Youtube, release it on vinyl, 8-track tape and wax cylinder, and see if a SWAT team will be breaking your doors and shooting your dog.
Since I am not a professional I would be able to get away with singing it even uploading it to Youtube but the moment I started selling it I would be in trouble.