Can a dental or medical office charge you for cancelling an appointment?

I called to cancel today, they had a recording that said ‘there is no charge for cancelling 2 days in advance’, my appointment was tomorrow. They tried to charge me $75 in the past for missing an appointment, but I called and got on the ‘short notice’ list so they waived that. In this age of recession, I think it’s messed up to charge like this, can they do it?