While he sounds a bit extreme, his premise is basically correct. If someone is given a right to use the labor of others with Government force utilized to ensure that conscription of labor, it ceases to be a free choice and can be viewed as a type of enslavement.
While using the term slavery brings up visions of men in chains forced to do the bidding of their owners, obviously we aren't going to see doctors in chains, however, in some forms of socialized medicine their labor, knowledge, and production does become a commodity owned by someone else, in this case the Government, to be used at that Government's demand, price, and prerogative with little, if any, regard in these areas given to the actual producer of the service.
The part that should worry most people is how simple it is for the Government to 'own' someone's labor, property, or knowledge. All they have have to do is call it a 'right'.