I'm of the opinion that his attempt to field the ball ended at the time he fell. The interpretation involving protection through a throw implies that the fielding attempt and throw are part of the same continuous action.
But there is no normal throw because he fell. We cannot give protection to a fielder for an indeterminate amount of time between his initial attempt and his first throw. Otherwise if a fielder started a rundown, a runner would be liable for INT until said fielder threw the ball.
Let me be blunt. There was nothing illegal about this slide. There was nothing malicious about it, unless you want to start tossing every kid who slides hard. There is no rule against taking a player out when it is done without violating any specific rule. 7.09e has a specific interpretation when hindrance is caused by a slide, which has already been mentioned twice. This was an incorrect call.
Let me break this down for you. A fielder can catch the ball in the field of play and go into any DBT (besides spectator areas) and the ball will remain live until one of three things happens: the fielder falls, the ball is dropped, or a throw hits something in DBT. There is nothing prohibiting a throw from those areas. There have been at least three people explaining this to you.