I agree with everything you said, but unfortunately the site can't know what may have caused disconnection. Many people would take advantage in crucial moments disconnecting, if you was the only losing the connection , most of the time you (or your provider) is the major responsible for your connection. I don't really have a plausible solution to this case.
Each case is different. Just remembering an example that happened to me in a tournament of 888 poker
this year, a Halloween tournament with 10,000 entries. In the middle of the tournament I was disconnected, and could not come back for about 10 min.
When I tried to return, the site said that the problem was in my internet. When I came back, almost the entire table (and at others tables too ) was disconnected, but the tournament went on. The few who won't disconnected were
stealing all the blinds, and had no replacement . In this case , which for me was clearly an error at site server, they would have to stop the tournament to normalize everything, but it was not what happened.