Can you handle scorekeeping without full storage permissions?

I’m creating a very simple Android game and handle my high score keeping like this:

This, however, results in the game requesting full read and write permissions to the storage system on play (even though I did not set this up explicitly myself). Is there any way to handle scorekeeping without this permission prompt? I don’t need any specific permissions apart from those needed to keep the score. Does this equal these storage permissions, then, or is there some way to handle it?