Hello Carmeron222,
It is possible and from what you wrote you did it correctly. To make sure you have the correct option, I have a screenshot below. I am making the default filter My Invoices. Once you check the This is the default view for this grid, the default filter will be for that filter and will uncheck it on the previous filter.
Try doing it again. This time keep the screen with the grid open. When you complete the Publish, you should see as screen like below. This will tell you have saved changes for the screen.
Greg