This is a reasonable requirement which many banks probably have. The reason is that after you deposit a check, ACH or direct deposit - they may be reversed after a couple of days (check bounced, payment canceled, etc). If you wire the money out, and then the check by which you got the money gets bounced - the bank is left hanging because money wired out is very hard to return. Wire transfers are generally irreversible unless its a mistake in the wire.
After 10 days, these transactions cannot be reversed and the money is bound to remain on the account, so you can wire it out.
By the way, it also goes for cashier's checks as well, I had a similar discussion with my banker (don't remember if it was WF or Chase) when I needed one based on a ACH transfer from my savings account elsewhere. They gave me the check, but said that its because I proved that the transfer was from my own account.