For wonkish, go google Diamond-Dybvig model.
But let's make it easier. Some people seem to think "systemic risk" here means the bank is related to other banks and therefore can affect the latter in a contagious process. Maybe I'm wrong, but Burhanuddin Abdullah and Anwar Nasution seemed to use this concept in their hearing with DPR's Pansus. According to their logic, since BC is small, it couldn't have systemic risk whatsover.
Some others believe it is expectation that really matters. (I got that impression from for example Boediono's and Miranda Goeltom's responses to questions from DPR's Pansus). As a depositor in Bank A, you, a risk-averse person (and by the way, that's a fair generalization), would feel anxious when you see people run Bank B across the street. No matter how small Bank B is and no matter how unrelated Bank A and Bank B is. The only connection between the two banks is what we call human expectation, driven by the act of observing something that you then expect might happen to you, too. Your reaction can vary. If, by any chance, you have the information that general situation is manageable (eg there hasn't been any news about world struck by crisis or something; or any other relevant information), you might not withdraw your money from Bank A. Yet. But, in many cases, you can't have full information on whether or not the situation is "manageable". It can take only a couple of depositors loudly saying "Gee, that bank is falling! This bank is next, I'm gonna withdraw!". Before you know it, Bank A is rushed, too. Then Bank C, D, so forth. It is therefore "systemic". This latter situation is sometimes affected by your perception on the authority, in this case Bank Indonesia and MOF. When you know (or are told) that BI and MOF are short of liquidity and fiscal capacity to deal with a crisis, your incentive to quickly withdraw and save your money at home rather than bank increases. In other time, you think BI and MOF can handle the situation well (even if Bank B is rushed, their depositors are saved, etc), in which case, your incentive to withdraw is relatively small.
So, it's about expectation. I'm more persuaded by this second understanding about the word "systemic risk".