Brainteaser 1625: Jolly sticks

From The Sunday Times, 31st October 1993 [link]

In a qualifying round of the European Ladies Hockey Cup held recently, each of the four participating countries played each of the others once. There were no draws. The final results looked like this:

If I gave you the score of the Holland vs. France game you could deduce the scores of all the other games. But if instead I gave you the score of any one of the other games you would not be able to do so.

This puzzle was selected for the book Brainteasers (2002, edited by Victor Bryant), where it appeared under the title “Qualifier“. The wording above is mostly taken from original puzzle, but I have slightly changed it using the book for clarity.