On the BT8500 not getting the option to allow the caller's number usually means the phone does not know the caller's number. That would also explain why she is asked to Announce. When she calls does the phone display her number, International or something else.
It isn't going to work until you find out why Caller Display isn't showing her number, or you change the Guardian settings.
As you suggest, calls may be routed via a third party, usually chosen by the caller for cheaper calls, so if her package of free international calls are with her telecom provider that doesn't seem something she'd need.
It is possible for callers to use a prefix to withhold their number or, if they arrange for their number to normally be withheld, to allow it to be sent on a per call basis. I don't know if this would result in CLI displaying International or Withheld.
Maybe if it used to work ask her if she made any change around the time it stopped working.