It just means that you could have hit more than just a 1 when training the account if you had like 30 str. As you can gain those STR levels even at your current stats without gaining a CB level
I mean I've seen quite a unique account at PC. 75 Defense and 75 Attack, 1 str. I think he was trying to go for 99 in both attack and defense...what a crazy guy! I believe he said his max was a 4 in his max str gear.
I would see if you can create something for random breaks within a span of 2 times. IE every hour to 2 hours it would take a break sometime between that at random. You said it also supports banking?