This is apparently incorrect. You need a reservation somewhere to join the 1 PM virtual queue. You must always enter the park you have a reservation at before "hopping" over to MK. So, as long as you have a reservation somewhere, tap into that park, and then go to MK, you'll be fine.
This is what Disney says:
The 1 p.m. virtual queue will be available to Passholders with a park reservation to any Theme Park for that day. As a reminder, Passholders must enter the theme park where they have a reservation prior to visiting Magic Kingdom Park. Or, on June 13, 14, 17, 18 or 20, they can enter Magic Kingdom Park without a reservation after 2 p.m.