Dogs placed in a minecart are able to invisibly telleport to the player while physically being still being stuck in the minecart.

To see this in effect: Get a dog or dogs into a minecart then walk towards any fire source, either lava or actual fire. The fire or lava needs to be 1 block above the block you are standing on (I.E. Burning nether rack placed on and not in the ground). When you get near enough the fire, the dogs, even though still stuck in the minecart, will catch fire and you can hear them taking damage.

I believe the reason for this is that when the dog is placed in the minecart, it causes them to stand (I have them in minecarts because they need to stand in order to kill skelitons constantly and not teleport to me) which makes the game think they can move and teleport.