The issue is money laundering laws. The bank only needs a statement from you as to the source of the funds for their reporting.

The bank is only the reporter, not the enforcer. Whatever you say or submit to them they will accept.

 

I had to send a pile of cash to my ex-wife in Canada. I choose to draw a Managers cheque on one bank and use a second bank to do the wire transfer. Better rates at the second bank.
Both banks wanted to see an email showing where the money was going. Neither bank looked closely at the documents. I think it was just a formality of filling in the blanks. They took copies for their files.
Go figure.