Would there be a difference between flushing the AFT fluid and dumping and refilling the ATF the normal way three times?

When you change your AT fluid, you're also supposed to change the filter.

To answer your question, flushing is more thorough than just draining and refilling several times; although this method should be adequate enough.

I disagree. It's not like the engine sump. You've got to flush it out to clear the crap out. It's not hard to do. 10L-15L of fluid, a new filter (external filter models only), a large socket for the tranny nut (size??) and a couple of tubes to direct the fluid from tranny cooler hose into a bucket and your set.

There is a writeup on this forum. Do a search. The process is really easy.