I'm going to say this even though I have no idea whether it makes sense scientifically or not, but then again, this is manga...
Anyways, my two cents are this. Obito had his special Uchiha chakra imbued into his eye, and considering that it was still in Sharingan form when he transferred it to Kakashi, is it possible that that chakra remained in the eye, and then spread through Kakashi himself? This would be substantiated when we see Obito seeing what Kakashi sees, seeing as a bit of the Obito UCHIHA chakra remains. So when Obito unlocked the Mangekyou, it wasn't coincidence that Kakashi did, it was a result of the connection, as many have already said.
Basically I'm trying to scientifically explain the connection, and I personally believe that seen this way, this is no plot hole.