And I think I've worked out what my problem is: perhaps it's yours too? I have unlimited local calling, but my area has 2 area codes (412 and 724) and only 412 and certain 724 central offices (exchanges) are covered by this plan. So I cannot use this phone to call two cell phones I own, that were originally provisioned to this address, because they have the "wrong" exchanges and aren't covered by unlimited local calling. I have to get a regional plan if I want to call them.
the message telling you to add a one and a zero plus the five digit code is referencing when long distance carrier access codes changed format (for example AT&T was 10288 and later became 1010288).
These carrier access codes were very commonly used in the late 80s and 90s when long distance calls were more costly and competing carriers were offering cheaper rates than Ma Bell.
As far as why you are hearing the message, it may be simply due to a misdialed number, or a network problem within Verizon's switch. If the problem persists, call Verizon Repair at 1-800-VERIZON.
Note: although you shouldn't have to dial a 1 for long distance on FiOS Digital Voice it can't hurt to try dialing a 1 first and see if the call completes. Traditional landline customers (whether on Copper or Fiber) always need to dial 1 for long distance calls.