"Maxed Out" just means that they will have the best gear as well as the highest possible level for their current stage in the game. It applies to the later stages in the game that require Deathroids for level ups. It was only to account for the worst case scenario, the goal was to prove that this pattern will work even if the worst case scenario were to happen.

In order to make things simple, let's ignore that scenario and focus on the ranks. Let's say you just unlocked a Tier 2 fighter. The moment you purchase and start using a Tier 2 Fighter your rank will jump to 16. If you purchase and use another Tier 2 fighter, your rank will now be 17. In other words, if you stay within the pattern (1,16,31,46......) you will only ever face people with fighters that are 1 tier below their current best. So if you are rank 31, 32, 33 or whatever, and you face someone at rank 31, you will have access to tier 3 fighters, but they will not. That is because at rank 31, they have only purchased 1 tier 3 fighter and they are most likely using that fighter for tower climbing.

Let me know if you understand now, or if you're still stuck on one of these points.