I had a friend at work who called out sick and was told by the supervisor that he couldn't. Is this allowed.

Unless the illness was protected under FMLA, yes, it's allowed.

I'm not necessarily agreeing with the action taken by the employer, but outside of FMLA an employee does not have a guaranteed right under the law to sick time.

Well, yes and no.

The employee can call out sick.

The employer can then fire the employee.

There are some exceptions. I expect none of them apply to this case.

I had a friend at work who called out sick and was told by the supervisor that he couldn't. Is this allowed.

It's also possible that there is more to the story than you know, such as that your friend has been frequently absent from work and the supervisor has had enough.