Can an unconscious person drink a potion?

PHB 153 reads:

Potion of Healing. A character who drinks the magical red fluid in this vial regains 2d4 + 2 hit points. Drinking or administering a potion takes an action.

By my interpretation, this means that while the rules are flexible in regards to who has to spend the action, they are inflexible in that a character must still actually drink the potion. In other words, any character can administer a potion to save someone else’s action, but their target must be conscious and able to drink.

I know part of a DM’s job is to apply common sense to my rulings, and common sense tells me that an unconscious person is more likely to choke to death than to swallow 4oz of liquid.

A few of my players disagree. Who’s right in this situation?