A security deposit you were paid, is your company liability with an offsetting entry as a deposit to the bank.
Equity is automatic, it is the difference between total assets and total liabilities. So with the exception of adding personal money to the business, or taking some out, you do not post to equity.
Glad to hear it was a previous accountant that gave you that advice. A bank account tracks the money you have, so when you receive a security deposit it should go up, a deposit. You do not just "put" a bank balance in there for the balance sheet.
To add the security deposits now is an issue. The account you used when you made the deposit of the funds has to be changed to a 'deposit due out' liability account. Of course that assumes your bank account is accurate now.
