I saw this happen just prior to the season 1 patch, it was in the low level group activity where the klingons and the feds are trying to kill an enormous clump of borg cubes and spheres and you had to scan 8 things before your weapons became useful.
Everyone was in Tier I ships, and there was a Galaxy class ship with an IKS name in red that was killing all the other fed ships left and right.
I have seen this several times in the "Borg Hunt" mission in the neutral zone at Admiral level while doing my daily. At the beginning KDF and FED start at the same spawn and several times I've seen Fed Cruisers with an IKS designation attacking Feds. I've have been wondering what this is for some time now. The issue definitely exists.
as far as a war zone goes when it makes two teams it just designates the opposing team as the opposite faction, instead of just having another fed team.
As far as a member of the opposing faction having a ship of their enemy my only thought would be that it relates to someone inviting you to their bridge. IE a fed goes to the sol system takes his ship close enough to the base to bring up the dialogue to beam down, then he invites a klingon to his bridge, and if there's a bug they may be able to select the beam out button, sending him to the sol station. As long as they weren't wearing a title, and the traditional klingon garb (color wise/Klingon Sash) they wouldn't really stand out.
I could also see sol or Qonos not being coded to have npcs attack or flag the member of the opposing faction, simply because the game isn't designed to let them be there. Also i dont know if they changed it yet but i remember seeing previously that they were gonna change bridges to avoid the killing fiascos, and the change could have been applied (not by intent) to all federation "interiors".
All that being said, the real give away for it being a bug/exploit will be when feds start showing up with klingon ships. I don't see to many klingons doing this except for the novelty of it. Plus a fed on Qonos will stand out like a sore thumb seeing as Klingons have 2 costume choices, and really only 1 if they're a female character.
Combine that idea with some random Fed players thinking they were playing in Starbase 24 again
There's no doubt that we KDF players would die quickly, but the chaos and tears that it'd cause would be well worth it!
... the only tears I remember came from klingon players during the end of beta event, begging starfleet for mercy so they can jump out of Sol again.
The poor targets not only made the mistake of jumping into Sol alone, but also in most cases didn't know that one could leave such an area while being dead.
Me and a few others would halt our fire sometimes as we didn't believe in continuous torture, but most players weren't that generous. And I have to admit it is quite an entertaining sight to see a Bird of Prey or a Raptor blow up within seconds due to being hit by weapons fire from about a dozen ships.
In all fairness though.... I'd really rather fight alongside the Klingons than against them. Victory parties are a lot more fun when some Klingons are around, they really know how to celebrate.
It has happened to me a couple of times. While waiting for my pvp que, I will go to Karrat to kill Feds while they are fighting Borg.
If I get killed and waiting to respawn and I get called into pvp by my que, I will respawn and can not target the enemy or they can not target me. Its got to be a bug or something. I did bug report it.
Yeah the Borg Hunt at Kerrat often switches a Fed player to the klingon side, but as far as I've seen they've still been in a fed ship, just on the other side. Maybe a glitch or more likely just a team balancing system.
What the OP is describing sounds like an exploit (yeah or maybe a GM) and if so would be worth trying.