This is allowed under Federal banking laws and does not give the bank free reign to make up their own rules.

Holds are commonly used to ensure full settlement on (large dollar amount) paper instruments, especially when combined with overdrawn account balances. It is partly to reduce credit risk and fraud risk. If an institution deposits a check and makes funds available same day, or even the next day, it's basically a short term loan on their books until the payor institution settles the check. If the depositor withdraws the funds and the check bounces, the bank takes a loss.

A combination of factors are used to determine the institutions risk appetite and triggers for applying a hold.

1. She overdrew the account because she likely maintains the balance near $0. It's probably an account that she does not use often and does not keep tabs on very closely (otherwise she wouldn't have overdrawn it)
2. She deposited a large check, in an account that probably has no history of this type of deposit.
3. The large check covered an overdraft. This is a red flag within the banking system for potential fraud. It will become an 'exception' and extra scrutiny will be applied.

Based on the hold limit, I bet the account was brand new and she possible used a check from outside the Federal Reserve region.