In the second lecture (Sharding Architecture) the Instructor talked about that config servers are responsible for even distribution of data and gave example using the Football players names. Does that mean that for any reason if there was uneven distribution of data, the config servers automatically will relocate data as it sees fit to make sure that data is equally distributed?
The config servers are responsible for the balancing of the chunks throughout the shards.
What the shards try to do is, if the balancer is running, to distribute the chunks so they are evenly spread.
In the case of 5 node shard, with 500 chunks, the balancer will try to move 100 chunks to each shard.
Now, data overall may not be even distributed. That depends on how good is your shad key.
To answer your question:
In case of shard distribution that is correct.