In addition to the above, check your state laws. Because a bank paid a check, that does not mean that the writer of the check (drawer) cannot have a claim after it is paid by his/hers/their bank.
In most states, the account holder has a period of time to review the statement and make a claim against the bank for a forgery, raised check, etc. This in many states is 6 months. If the check you deposited was stolen, counterfeit, etc., the account holder could return the check to the bank with an affadavit of forgery, etc. and have the check returned to PonyBank. After your account is charged-back, you would have a claim against the writer of the check.
Just saying that while credit has been given, if there is a forgery or other crime committed, you can get a very unpleasant surprise for about 6 months.
I agree that if you're unsure, you should send the check for collection with the instructions "wire fate".