To answer your questio, what you heard is correct. As long as you are online at the beginning and the end of the game, losing internet in the middle will have no effect. There will be no need for a restart just because you lost internet in the middle of the game.
As far as punishment for restrats, you can't be light. Restarts cannot be tolerated. In leagues that I run, the owners are supposed to let me know if there game freezes and they have to restart. If not, it is counted as though they quit. After one warning (in year 1 only), I boot them on the second restart.
It is just my opinion, but allowing restarts can ruin the entire OD if it is not tightly controlled.