With the proliferation of cell phones and VoIP there is no guarantee your call is going to the location indicated by the area code. With that, there is only about a three-hour window that would ensure a non-intrusive call (presumming you are even in the US).
Personally, I use VoIP and program acceptable times to pass a call through otherwise the only choice is voicemail. Now if I can only find a way to filter calls to the hotel phone (other than pulling the plug).
A 6:30am phone call is tough, but I don't fault the property for wanting to confirm such a reservation. Maybe next time they will consider an eMail instead.