On my first playthrough, just bought the secret base, and after mucking around with other peoples’ bases I noticed that the Level Trainer seems to cost me no money in my own base (battling the 20s Audinos nets me Y1200 instead). He neither prompts me to pay nor does the appropriate deduction occur.
In other peoples’ bases the same NPC charges me the Y400/10lvl as usual.
It’s a feature. Level training in your own base costs you nothing, but using it in other bases is still a cost. If you beat the level trainer in a friend’s base they pay you, and in your own base, he still pays you as well.