Stock options closing to the current market price of underlying are always the most active and traded the most. The open interest of these calls/puts become the most volumes very soon. This is especially true during the last several days before expiration while these options are cheap.
For example, when a stock trades at 100, the 100 call/put have the most volumes. When the stock price drops to 80, the 80 call/put have the most volume. Most of the 100 call/put is closed.
Their theory is that IF THERE IS NO BIG COMPANY ANNOUNCEMENT, in which case the stock price will most likely stay at about 100. And of cause the stock will be able to close at about 100 on the expiration day.
All options are about possiblities. If you follow their theory too early than expiration, you have more chance to loose money, whcih translates into big risk. If you follow their theory too late than expiration, you can only win a little and may lose a lot which translates into big risk too.
I do notice there is a strange observation while I don't agree with your max pain theory.
Most of the time the stock will be closed very close to a strike on expiration day. For example, if the enclosure strikes are 95 and 100 and stock is 97 now. It will be closing at 95.xx or 99.xx most likely tomorrow.
I think this is a scam but I haven't follow them for a long time. Just a funny thinking.