<putting on flak jacket> This issue has as much controversy as any on this board. You will find mild to rabid adherents to both schools. I think if you have an electric drill, then dropping the pan, changing the filter, adding a drain plug to the pan (1/2 " drill and a $5 plug added for future use) and putting the newly plugged pan back on and refilling the few quarts you drained out... and several additional drains and refills in the weeks/months ahead is a good method.
Letting the Trannie pump pump out old fluid and add new as it does is not a bad method, depending on the age and condition of the fluid in the trannie....
I am not in favor of a machine flush on a high mileage trannie. I believe (without any data to back that up) that it may loosen too much debris.
Hope this helps.... there is no "gold standard" here, IMHO.
Smarter people than I am may disagree with me. I fully support their right to be wrong <grin>. Kidding.