I haven't run into too much problem in regards to PVP while out hunting for pets. Since the "old world" isn't as hip a place to be anymore, most of the zones are pretty void of people, which makes it easy to move around and battle in peace.
The only time(s) that I've had a run in with horde is while I was battling in Pandaria. I managed to get away each time (just barely!), but it put a damper on my Pet Battling experience. Thankfully, the exact same wild pet that I was fighting respawned (both had rares on their team lol). So it wasn't a complete downer.
When I mentioned to guildmates that horde were poking at me at the most inconvenient times, though, they were pretty shocked that others could attack someone engaged in a Pet Battle. My guildies thought that you would be phased out, and were surprised to hear that the person in a Pet Battle just stands out in the open for all to see (and attack).
I had to explain that yes, you aren't invulnerable, but you do get a shield that reduces incoming damage for a short period of time while you gather your bearings.
This didn't seem to ease their disbelief, and as one guildie put it, "That's not player vs. player. That's like player vs. statue."
That comment stuck with me. It really IS like someone hitting a statue and then that statue comes to life. Sure the person in the battle can sometimes see the other person coming, but what choices does the battler have to truly make it "player vs. player"?
Forfeit the battle, lose the current pet team they were up against, just to fight off the enemy player? That doesn't seem like a very ideal choice to me. At least if the player stays in the Pet Battle and gets knocked out by an attack on them, the same exact wild pet will respawn. If they forfeit, the companion disappears.
That being said, you pretty much are frozen in place until the first attack kicks you out of the battle. So a statue is a pretty accurate description.
I don't fully agree with this, and I fail to see how this promotes healthy world PVP (more like world PVS, player vs. statue lol), but I have to admit that I can't see any way around it.
Developers can't make you immune to player contact while in a Pet Battle because that would be too overpowered. It would allow a quick and cheesy escape from actual PVP.
It can be frustrating to be up against someone of the opposite faction, but suddenly that person disappears or phases out. Making a Pet Battler phase out would be the same thing.
It would be equally as irritating if you were immune to all damage upon entering a Pet Battle. Find yourself in a sticky situation? Get out of combat, find a wild pet, enter a Pet Battle, and bam! You're safe. Indefinitely. Kind of a cheap get-away, yea?
So while I don't exactly like it, I do understand the need for this design model. It can be frustrating and discouraging if on the receiving end, but it seems to be the fairest compromise.