Considering you don't work for Riot support either, your comment regarding "other companies" is irrelevant.
The phrase "manual audit" could mean anything from a team of 5 people sitting down, watching every game of the last 10, and then making a determination (at best) to one person looking at chat logs and making a decision in 10 seconds (at worst). Based on the number of times I've gotten a "your reports helped punish someone" after I report a troll/intentional feeder, vs the times I've gotten one after I report someone being toxic, vs the times I don't get one at all after reporting someone, it seems that their "manual audit" consists more heavily of looking at logs (chat, buy, kills, etc) than it does looking at entire games.
Support nunu and singed were both triggered by very specific play conditions and styles. In these instances, Riot was able to use log-searching (for a player who was assigned/chose support, took nunu as a champion, took smite, and followed a certain build path, smite usage, etc) and if it met a threshold a manual review could be done. This does not work for many types of trolling.
Most trolling isn't the obvious kind that can be found by a computer (buying 6 boots, buying 3 tears, etc). Much of the trolling/refusal to play role is much more subtle - Last hitting minions "accidentally" but repeatedly through the whole game as your ADC has asked you to please stop; a full health teammate refusing to block caitlin's ult repeatedly, etc. These are not visible to a computer. There is no way a log file (chat, buy, otherwise) would show this type of trolling. Thus, manual review of these reports should be conducted every time, not just when specific conditions (such as support nunu/singed) are met.