Andy,
you need to place the word "value" after the word minimum to make your statement correct.
"1K is the minimum value load" or conversely you could say "1K is the maximum load".
It all comes down to the proper definition of minimum and maximum load.
A maximum load has a low value. In order to increase the load you decrease the resistance. Think about what you need to do to load something down.
A minimum load has a high value. In order to decrease the load you increase the value. Think about how you reduce the load seen by the source.
dave