The thing is, it's not even a matter of trust. The fc setting are not some trust-test or intention-test that lets you see who wants to take things out the bank. They are there to tell others "go ahead and help yourselves even during the times I'm not there to hand it to you". They are a formal permission to take gil, items or company credits for any use without asking a second permission. It is not uncommon to have one tab set open to everyone full of cheap minions, Krakka Roots or cheap food to be freely used by newcomers as kind of a welcome gift.
What I don't understand is if people want newcomers to contribute a certain amount of credits before using them, why give them a silent message that they can use them straight away? If people don't want items taken from the bank for personal use, why give a silent message that it's allowed? It's a form of miscommunication. Those permissions, while restricting people, also convey a message. Fc leaders expect people to read their minds and double-check about the bank and credits and publicly crucify anyone who fails to do so, when the leader had every tool available to inform people properly and yet chose to misuse those tools. They are not "victims" of thievery when someone takes a couple of items. They are not "robbed" when a minuscule amount of credits is used for personal use. They tell people that items/currency can be taken from the bank and then withdraw that permission in a whim, blaming the person who believed them.
Why on earth would you tell people that they can take things at their own accord if you want them to ask permission each time? Just... tick the damn box so they know they are not allowed to take things by themselves and have to ask permission. If you invite people for a party and they happen to eat from the table you set up for guests, you can't blame them for robbery when they don't ask permission for every crisp and popcorn. If they empty the crisp and popcorn bowls into their bag, stuff their pockets full of beer cans and pile all the pizza on their arms before scooting out the door, that's a bit of a different story. But that's not what the OP did.
A situation where a long standing member of the fc clears the bank clean of everything before they hop servers is very different and I don't condone it. The whole bank is emptied in a malicious way, which is different from taking only what you need/like from the bank for personal use or spending a small amount of credits on something nice (whilst leaving enough for buffs+airships and other people's personal use). SE could prevent fc bank clearing by allowing the fc leaders to set quantity limits on top of the existing limits (daily limit of item stacks per tab, daily gil limit and daily credit limit). This would also further allow communication about what is deemed acceptable in that specific fc, because believe it or not free companies have different ideas about the correct etiquette of taking things from the bank.