FWIW (maybe not much) but maybe something is happening which is decided in the arena log-in phase.
I was involved in the dual cv incident. It appeared to me that the "virtuality" that you experienced depended upon whether you logged in before or after a triggering event/time. I noted then, that people that had been on for the previous hour or so could see the cv sailing across the land. This cv was perfectly functional for us with the exception that we couldn't control its heading. People that logged on after it was apparent that we had a cv with a split personality would all see it at the same position (at a different place to those who were on earlier).
It may well be that the time you log on affects which virtual world you are experiencing. If the invisible fighter didn't appear in your world because he had just logged on, then he wouldn't appear to your squaddies either. Relogging may bring the "worlds" into line. Of course the only way to test this from our end, would be for somebody to relog quickly and then gun for you. (There are flaws in this that should be apparent as well, but it's one test worth a try).
Now cv's and invisible planes may well have different causes and maybe invisible LVT's have a different one again. I have a film of an "invisible" LVT. I was RTB after an attack on a CV and suddenly started taking mg fire. Nothing about. Eventually I died. Killed by Teufl I think it was. As I was near a shore battery, I jumped in for a look around. Amazingly I could see a boat wake, but no boat moving around.
I've checked the film and reveals that there were 2 LVT's there. The film doesn't show either the lvt's or their wake but does show shots being fired at the position of where I could see the wake. If I remember correctly, at some point at least one of the LVT's became visible. I cannot remember if this had anything to do with relogging though.