Um, that is hugely false. Supports rarely take cs yet they can be the only person the team to get an S+, S, or S-. Also, Riot said that it takes into account your role and the attributes of that role.
The main thing is NOT to loose your tower because as the "guardian" of that lane is too ensure that it stays strong (jg is an exception of course).
Supports need to ensure their team gets kills and is able to leave safely (sometimes at the cost of their own life).
ADC's need to be able to push lane and decimate the enemy team while not feeding.
Top (same as ADC, also needs to start team fights if tanky)
Mid (same as other lanes, can start team-fights)
But, you also have to help with objectives.
Top / Bot help jg with leash.
Dragons / Barons / Rift heralds
Towers / Inhibitors
They take into account farm, items built, kills, deaths, and assists.
But, they mainly base stuff off of if you played your role correctly and efficiently. Sometimes it takes getting that right team. For me, I have a partner (Leona supp) that decimates bot lane with me (MF adc). Our partnership has already earned us 3 S's in a row (I'm S5 and he / she is unranked doing placements today).
Mainly, the more that you are helping with, the more that you will be higher graded. As for your problem, the ADC's farming ties in with their role. They need to farm, push lanes, build items and so forth. Several factors played into that, not just the farming. Someone can have poor farming but still get an S grade. I have read multiple articles and the authors agree that the top three things are:
- K/D/A (Kills are weighted less than deaths)
- Lane Push (Part of your role)
- Teamwork (Umm, this is a team game so...)
But, if you have read this far thank you. I know that this is just an opinion, and no one needs to take this as the truth, but don't just believe that farming is the top thing in LoL.