Unfortunately, you've let the cat out of the bag and he'll go find a witness who saw one...
I dare him.
As you might have guessed if you know anything about VTOL, an aircraft like this isn't
seen as much as
heard. It's not exactly going to fit the narrative, no matter how heavily witness statements are quote-mined or interpreted. And it would have no chance to escape unnoticed.
Vectored thrust isn't the right solution to this problem anyway, as we already commented some months back. It helps with rapid changes of attitude, short-field performance, and hover, but it has almost no impact on an aircraft's ultimate turn radius. If anything, the massive fuel consumption and strict thrust-to-weight requirements VTOL places on the airframe will actually hurt -- turning in a VTOL tends to be limited by inlet performance, whereas a more conventional aircraft wouldn't have this problem.
A specially built F-15 with a super-duper hotshot pilot, I might believe pulling a brief 12
g maneuver, for instance. That will never happen with a Harrier, and certainly not a VTOL/vectored thrust transport.
If this is really what the Pilots For Truth have come up with, it makes me wonder if they know anything about aircraft at all.